AmalgaCloud: Social Network Adaptation for Human andComputational Agent Team Formation

Kirill Osipov*Department of EECS

University of Central FloridaOrlando, Florida

Email: karl@knights.ucf.edu

Gita SukthankarDepartment of EECS

University of Central FloridaOrlando, Florida

Email: gitars@eecs.ucf.edu

ABSTRACT

Many complex problems can be solved through aneffective organization of human experts and softwareagents connected by a social network where each nodecontributes the unique skill set needed to enable ahigher order problem solving capability of the group.Recent work in crowdsourcing applications based onenterprise social networks (e.g. PeopleCloud) hasshown that the group problem solving approach canbe extended to enterprise and potentially Internet-wide scales. However, systems operating at suchscales assume that candidate group participants makedecisions about which groups to join based on limitedconnectivity and local information.

This paper focuses on the relationship between net-work adaptation for candidate group participantsand performance of problem solving groups. Wedemonstrate that systems that expect to form groupsby engaging participants equipped with diverse skillsets require more sophisticated network adaptationstrategies than what can be expected based on previ-ous research. To address this need, we evaluate a setof network adaptation algorithms for crowdsourcingand present some empirical results from a simulationbased study.

I INTRODUCTION

Problem solving activities are increasingly based onself-organized groups (communities or teams) thatcollaborate across functions, divisions and levels oftheir respective organizations [1]. Team formationis growing in importance as a business problem [2].In the area of human team organization, the oper-ations research (OR) field has developed several in-teger linear program formulations specifying optimalteam composition which can be solved using branch-and-cut [3], approximation heuristics [4], genetic al-gorithms [5] or simulated annealing [6]. Advancesin social graph data mining coupled with traditionalOR techniques have enabled novel solutions to theproblem of human team formation [7]. Team forma-

tion supported by social network adaptation has beenshown to increase team [8] and organizational perfor-mance [9] [10].

This paper reports on results of experiments used toguide design of AmalgaCloud [11], a research projectby the authors to prototype an internet service fororganizing problem solving teams from a social net-work of human and computational agents on a ba-sis of a structured problem definition. An agent inAmalgaCloud has expertise (skills) and can form orjoin teams with agents having complementary exper-tise from its social network. The social network hasa continuously changing structure as agents use al-ternative strategies to modify network connectivityin a search to improve their problem solving perfor-mance. We explore alternative network adaptation(modification) strategies and their relationship to theAmalgaCloud problem solving performance to betterinform AmalgaCloud design.

Our contributions.

1. We describe an extension of the team formationalgorithm studied by [7] to a parallel setting wheremultiple, independent agents self-initiate team forma-tion proposals and choose between alternative pro-posal variations to maximize their team formationperformance.

2. We introduce a system (AmalgaCloud) to sup-port team formation by multiple, concurrent, inde-pendent agents and describe design choices related toimplementation of the system. We describe simula-tion based experiments for agent network adaptationthat can inform system design.

3. We provide simulation based evidence in supportof network adaptation policies that take into con-sideration agent’s knowledge of its performance ontask completion (performance-based strategies). Wealso show that commonly used network adaptationpolicies based on preferential attachment (structure-based strategies) should not be assumed as effectivefor team formation that relies on agents with multiple

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skill sets.

4. We report measurements of comparing both struc-ture and performance based network adaptation inconjunction with the extension. The measurementsare interpreted and presented as design guidelines forthe AmalgaCloud.

Roadmap.

The rest of this paper is organized as follows: in Sec-tion II we review salient features of AmalgaCloudand outline issues and challenges faced by the authorsin applying existing research results to AmalgaClouddesign. We focus on scalability of the exiting researchresults relative to increase in the number of uniqueskills per agent and measure whether the structuraland performance based network adaptation strate-gies proposed by [9] [10] remain effective in presenceof exponential increase in the space of potential skillsconfigurations. In Section III we provide a formaldefinition of the team formation and network adap-tation models. In Section IV we present the experi-mental approach to evaluation of alternative networkadaptation strategies. We review related work aboutproblem solving with systems of agents in Section VIand discuss our results in Section V. We conclude inSection VII.

II AMALGACLOUD

As a detailed technical description of AmalgaCloud[11] is outside the scope of this paper, we providehighlights of the salient features of the system design.A formal, mathematical treatment of the models fortasks, skills and agents will be provided in the latersections of the paper.

Structured problem definition. The Amalga-Cloud system is designed to support a restricted cat-egory of problems that exist outside of the systemboundaries, are specified in a predefined structuredformat and can be solved by multiple teams engagedconcurrently and independently in problem solvingactivities for a restricted period of time to arrive toa solution. In formal specification for AmalgaCloud,we require that problems are:

• finite, a problem must be solvable within a fi-nite time interval which is given prior to thestart of the problem solving activity.

Fig. 1. AmalgaCloud is a research project by the authors to prototype

an internet service for organizing problem solving teams from a social

network of human and computational agents on a basis of a struc-

tured problem definition. The figure is the relationship diagram for

AmalgaCloud concepts, clarifying the terminology and the relationships

between terms. The arrow labels should be read in the direction of the

arrow, e.g. Task is a type of a Problem. The arrow represent a one-to-

one relationship, unless one-to-many relationship is specified using the

1...* notation. One-to-many notation should be read in the direction of

the arrow e.g. one Agent has many Skill(s).

• scoped, a problem must have a limited scope interms of the maximum number of agents thatmust participate in the problem solving activityto produce a problem solution.

• verifiable, a problem must have an observer (orobservers) to accept or reject a proposed solu-tion; a rejected proposal is considered not tobe a solution to a problem. In a given problemformulation an observer agent may be required.Alternatively, the accept or reject decision maybe performed by a shared observer agent.

• isolated, a problem must be solvable by mul-tiple, isolated and concurrent problem solvingactivities.

In this paper, we will use ”task” to describe a problemthat has these properties. The structured problemdefinition describes each task as consisting of multiplesubtasks. A subtask can be performed (completed)by applying a specific skill, i.e. there is a one to onerelationship between a subtask and a skill. A resultis a completion of all subtasks for the correspondingtask. An illustration of these concepts is provided onFigure 1

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This formalism can be used to describe a broad cate-gory of IT tasks related to service delivery and trou-bleshooting in complex IT environments [12] [13]. Forexample, a task many involve a team of experts withskills in networking, hardware, operating systems andapplication software working together to identify theroot cause of a decline in application performance.The isolated property of the problem ensures thatmultiple teams can produce independent (i.e. createdconcurrently and in isolation) results. The resultscan be aggregated to identify the most frequently re-ported or the most likely root cause of a problem.

Other aspects of the structured problem definitionare covered in more detail later in this section.

Fig. 2. The structured problem definition (SPD) introduced earlier in

this section includes information about the task to be performed, about

the agents that must perform the task and about the result. The solu-

tion specification part of the SPD, consists of 1) constraints, which are

inclusion/exclusion rules for agents, agent teams and the result; and 2)

criteria, which are rules (objective functions) for specifying preferences

over the space of potential solutions. For example, an agent team con-

straint may exclude any team formation solutions that have less than

three agents on a team; a criteria may specify that a team formation

solution should have a team with as few members as possible, as long as

the team has all the specified skills for a team. The result part of the

solution specification allows for additional restrictions such as ensuring

that a team can produce a result within a specified period of time

(constraint) or within as short of a time period as possible (criteria).

Social network of problem solving agents.AmalgaCloud assumes the existence of a social net-

work (graph) where nodes represent human or com-putational agents along with their skill (expertise)profiles. For example, for a human agent the skillsprofile may include ”reinstall operating system” whilefor a computational agent the skill may be ”report onan operating system memory utilization”.

Existing research on team formation using social net-work data assumes availability of the entire socialgraph to the team formation algorithm [7] [14] [15][16] [17]. However, this assumption is not appropriatein the AmalgaCloud setting where individual agentsworking in parallel, with only a limited visibility intotheir own social graph connections decide to form orjoin teams. We chose to eliminate the assumptionthat the entire social graph is available to an agentfor the following reasons:

• computational cost ; as shown in [7], optimalteam formation using a social graph is an NP-Hard problem. While polynomial approxima-tion algorithms exist, it can be too computa-tionally expensive for an agent to identify bestcandidates for a team from the entire socialgraph within the time constraints of the struc-tured problem definition.

• data and communication limitations; the datadescribing the social network can be too largeto duplicate, take too long to transfer to thelocation where it is analyzed by the team for-mation algorithm or the underlying communi-cations network latency can be too high for thepurposes of executing the team formation algo-rithm within specified time constraints.

• contention issues; in cases where the socialgraph is kept in distributed storage and the so-cial graph read/write operations are requestedby agents over a communications network, itis necessary to address a range of contention is-sues resulting from multiple agents making con-current requests by the team formation algo-rithm. The issues include: 1) ensuring synchro-nized access to agent team state (e.g. availabil-ity to join a team); 2) resolving conflicts due togeneration of multiple team proposals where asingle agent is offered to participate on multipleteams; 3) scheduling agent’s participation in ateam based on task duration and task start timeas specified in the structured problem defini-tion; 4) implementing the previously describedissues in a computationally efficient manner.

• integration challenges; an AmalgaCloud agent

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may participate in social networks from multi-ple independent providers. Thus it is desirableto ensure aggregation of the agent’s social graphacross the providers. While aggregation can beachieved by individual agents operating on theirown data, integration and aggregation of full so-cial graphs from multiple providers may not befeasible due to privacy and other concerns.

Existing research argues against the idea that anagent in a social network should have visibility of theentire graph. Based on an assumption of an agentthat operates with a finite time budget and must relyon a priority queue for scheduling its activities, [18]showed that there exists an upper bound on stable so-cial relationships (similar to Dunbar’s number [19])for agents in a social network. We apply this evi-dence to AmalgaCloud design to ensure that agentshave limited visibility of the social graph and canform teams with the agents in their immediate socialgraph vicinity.

Thus, in AmagaCloud, existence of an edge betweenany two agents represents bidirectional awareness be-tween them. An edge also indicates potential for twoagents to participate on the same team in a problemsolving activity. This collaboration potential betweenany two agents is defined in terms of the existence ofan edge because during the team formation process,an agent may join or initiate a team based only on theagents that it knows. An edge may optionally haveadditional relational information associated with theagents, for example communication cost or records ofpast interactions.

Team formation. A formal description of the teamformation problem will be provided later in this pa-per. Intuitively, team formation describes a processfor selecting a group of agents from the social networksuch that the team formed by the identified agentsmeets one or more requirements, which must includehaving the capability to perform the task specifiedin the problem definition. Other requirements maybe derived from the information specified in the so-cial graph edges between the members, for examplecommunication cost, history of past interactions orpresence of common social network neighbors. Dur-ing team formation, the agents are only consideringjoining teams that are in the agent’s immediate (di-rectly connected) network neighborhood.

The problem solving activity interactions that takeplace in a mixed team of computational and humanagents following team formation are outside the scope

of AmalgaCloud; [20] describes how interactions canbe implemented in mixed systems.

Network adaptation. Several studies have empha-sized the role of the agent’s social network struc-ture and the degree to which the structure influencesagent problem solving performance. In the contextof team formation, networks with short average pathlength [21] [22] [23] and a hub structure [21] [22] leadto greater efficiency in forming teams and to greaterdiversity in team composition [24] [9].

In AmalgaCloud, an agent cannot observe the en-tire social network and thus cannot make decisionsto modify its connectivity to other agents based onglobal social network measures mentioned in the pre-vious paragraph. As part of AmalgaCloud design, wehave considered that agents may need to perform up-dates to their social network connectivity using twoalternative strategies. Some strategies are structurebased, where an agent considers the number of andthe topology of connections of its neighbors. An-other category is performance based, where an agentmeasures its frequency of participation on problemsolving activity teams to corresponding frequency forother agents. Thus, to inform the implementation forhow agents modify their social network connectivity(network adaptation) in AmalgaCloud, we have de-fined a set of simulation based experiments describedin more detail in Section IV.

The lifecycle of the AmalgaCloud platform consistsof team formation events, sequential or concurrent.Network adaptation is defined as agent initiatedchange in the social network connectivity at the timebetween the events to enable the agents to prepare forfuture problems and future team formation events.To represent limited attention and workload capacity,agents have an upper limit on the number of possibleconnections to other agents in the network. Thus,once an agent has established a sufficient number ofconnections to reach the upper limit, network adap-tion serves as the only mechanism available to theagent to improve its problem solving performance.

Design considerations. We focus on problem solv-ing systems that are designed to be open and dis-tributed, defined by [25] as ones where the structureof system itself is capable of dynamically adaptinggiven a problem and where system components (hu-man or computational agents) are not known in ad-vance. While in MAS [26] information about skillsets for agents is known at application design time,our prototype is more similar to PeopleCloud [12],in that we can collect information about both the

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task and the skill sets of its social network partici-pants at system runtime. Information about the par-ticipants can be collected dynamically from externalsocial network data sources and is processed againstconstraints (e.g. history of participant contributions,knowledge expertise, participation levels) to identifythe right agents for a given task.

Existing research shows that there exists the need fora team formation platform that can support a rangeof alternative optimization formulations [7] [14] [15][16] [17]. In AmalgaCloud, we extend the structuredproblem definition (SPD) to include a collection ofconstraints and criteria that collectively restrict andrank possible solutions to the team formation prob-lem. The solution specification part of the SPD, con-sists of 1) constraints, which are inclusion/exclusionrules for agents, agent teams and the result; and 2)criteria, which are rules (objective functions) for spec-ifying preferences over the space of potential solu-tions. For example, an agent team constraint mayexclude any team formation solutions that have lessthan three agents on a team; a criteria may specifythat a team formation solution should have a teamwith as few members as possible, as long as the teamhas all the specified skills for a team. The result partof the solution specification allows for additional re-strictions such as ensuring that a team can produce aresult within a specified period of time (constraint) orwithin as short of a time period as possible (criteria).

There exists a broad range of research on how to usecentralized matchmaking agents for solving problemsby relying on multiple problem solving groups work-ing in parallel [26]. In MAS, identifying the rightteam for a given task (team formation) can be per-formed by using a specialized matchmaker (interface)agent [27] or through peer to peer sharing of goals andplans across agents [28]. In contrast, team formationalgorithms described in [7] and extensions [15] [16][14] [17] [29] rely on a single, central entity with aglobal view of the social network of candidate teammembers. It is unclear whether the centralized tech-niques can apply at levels of scale and dynamicity insystems intended to service large enterprises or theentire population of the World Wide Web.

Decentralized, peer to peer based approaches forteam formation have greater potential to scale tolarger pools of candidate team participants. Someof the MAS solutions have relied on peer to peer

based team formation, using plan and goal sharingacross computational agents [27]. Some studies focus-ing specifically on team formation [9] [10] [30] havequantitatively evaluated the relationship between al-ternative team collaboration network structures andoverall effectiveness of groups in solving problems orperforming tasks. These studies examine team for-mation dynamics, i.e. the changes in collaborationnetwork connectivity over time as collaborators seekto leave and join possible groups in order to improveboth their local and system-wide problem solving per-formance. While the peer to peer based approaches toteam formation have demonstrated greater scalabil-ity, the agents are faced with the problem of decisionmaking on the basis of limited information about theagents within their local connection vicinity.

It is desirable to specify skills at a sufficiently finegrained detail level so as to avoid ambiguity. In ad-dition, the skill set may grow at system runtime asparticipants list or acquire additional skills. How-ever, the increase of the participant skill set leads toan exponential growth in the number of the potentialgroups where the participant may be included1.

III MODEL FORMULATION

In our simulation model, there is a population of Nagents represented by set A = {a1, a2, ..., aN}. Eachagent is connected to a portion of the agent popu-lation via a social network which is modeled using asymmetric adjacency matrix E, where an element ofthe matrix eij = 1 indicates an undirected edge be-tween agents ai and aj . In the paper we distinguishbetween first order neighbors of ai defined as N1

i ={aj : eij = 1, j 6= i} and second order neighbors, de-fined as N2

i = {ak : eij = 1, ejk = 1, eik = 0, k 6= i}.

The degree of an agent ai, is denoted as di and rep-resents agent’s degree of awareness of other agents inthe network. It is measured in terms of number ofedges incident to the agent and is equal to |N1

i |. Asexplained in more detail in subsection 2, each edgealso represents potential for collaboration betweenany two agents because an agent considers only itsfirst order neighbors during the group formation pro-cess. Agents that operate under constraints of finitepriority queuing and limited time resources have up-per bounds on first order neighbors [18], which wemodel as maximum permitted degree Di for an agent

1Consider a social network where a vertex (node) represents an agent and the vertex degree d stands for agent’s awarenessof d other agents in the network, each edge representing a potential collaboration. Under the assumption that the agent repre-sented by the node has SA skills, the agent may offer any of its 2SA − 1 subsets of skills to a collaborator. Considering all ofits d potential collaborators, the agent may be a candidate for at most d(2SA − 1) collaborative groups.

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ai. Note that this constant is inversely related to thelower bound for agent’s ai cost of maintaining a con-nection to another agent, Ci = 1

Disuch that the total

cost over all the connections has to sum to 1.

Each agent ai has a set of skills Si which is a sub-set of size SA sampled randomly from a uniform dis-tribution over a set of the universe of skills S. Asdemonstrated by [31], this binary skills representa-tion includes more complex models (variable, addi-tive, multiplicative) as special cases. In this paper,we focus on the uniformly distributed skill sets tocompare our results to those in [9] [10] which use thesame approach. In Section VII we describe how weplan to extend our simulations to cover alternativeagent skill set models.

The agents interact over multiple time steps in a sim-ulation. At every time step ts of the simulation, a sin-gle task Tts is randomly generated by sampling with-out replacement from a uniform random distributionof the set of skills S to generate a set of predefined sizeTA. A set of agents (group) G = {ak, ..., al} is said tobe capable of executing a task T iff T ⊂ Sk ∪ ...∪ Sl.In all of the simulations described in this paper,SA < TA so that more than one agent is requiredto execute any given task. Every Tts is broadcastto all N agents and more than one group of agentsmay have the skills (potential) needed to execute T .As described in more detail later in this paper, thequantity of these potential groups is one of the keymetrics for evaluation of alternative network adapta-tion algorithms.

The model avoids concurrency issues by merging thesteps related to formation of a team and execution ofa task into a single time step of the simulation. Onceall of the potential groups are identified, every agentcommits to (joins) one of the groups using the algo-rithm described later in the paper. As long as a teamhas enough committed agents capable of executingTts then the team is considered to have executed Tts

at the conclusion of the ts step. Given the focus ofthis paper on Internet scale team formation, this for-mulation permits the possibility that multiple groupsmay complete the task in parallel. While it is possibleto introduce coordination or election mechanisms toensure that a task is performed only once, this topicis outside the scope of this paper.

1 INITIAL SOCIAL NETWORK CON-NECTIVITY

To establish connectivity, all agents are randomly as-signed a position on a square grid with side of size√N (based on the N value from Table 1). Distance

between the agents is measured under an assump-tion of toroid connectivity between grid’s edges usingManhattan distance measure, Dij . For every agentai, an undirected edge eij is established to every otheragent aj , as long as Dij is less than or equal to a pre-defined constant D (see Table 1). For every agent ai,the initial N1

i connectivity configuration as explainedhere is identical for all simulation scenarios describedin this paper.

The algorithm implementing this connectivity config-uration is identical to the random geometrical graphgeneration approach followed by [30] [10]. Alterna-tive methods, such as random graph or preferentialattachment [21] can be used to create the startingconditions of the network structure. As explained inSection VII, this is an area for future work.

2 CANDIDATE GROUP SELECTIONAND GROUP FORMATION

Since agents are operating on the basis of limited in-formation about potential groups, every agent mustmake a decision about which groups can solve thetasks and which groups the agent should join to exe-cute the task. At every time step of the simulation,an agent ai knows only which skills are available toagents in its first order social network neighborhoodN1

i . Before joining or forming a team, an agent aimust compute Gi,ts which is a set of potential groupsthat have the skills needed to execute Tts. Agent aicomputes the intersection of the sets Si and T andwhenever the intersection of the two sets is non-empty(i.e. the agent has at least one skill needed for thetask), attempts to perform the computation of a setof candidate groups that the agent expects to executethe task. The computation problem is equivalent toan optimization by minimizing the sum of indicatorfunctions2 which specify whether an agent aj ∈ N1

i

should be in the potential team set:

minimizeN∑j=1

IGi,ts(aj) (1)

2The indicator function of a subset A of a set X is a function IA : X → {0, 1} defined as IA(x) = 1 if x ∈ A and 0 otherwise

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subject to the constraint

Tts ⊂⋃

k∈Gi,ts

Sk (2)

The equations 1 and 2 are an example of thewell known minimum set covering problem [32](MinSetCover). In this instance, the objective isto find the smallest possible set of agents such thattheir respective skills Sj ”cover” the skills required fora given task T . While set covering is a classic exam-ple of an NP-complete problem [33], it has well knownapproximate solutions [34] and in context of boundedsocial network neighborhoods can be solved exactlyand efficiently using industrial scale solvers [35] .

An agent can both initiate its own team and be in-vited to participate in a team initiated by anotheragent. Given any two agents ai and aj , ai could be amember of Gi,ts or Gj,ts. We will refer to groups inGi,ts where ai is a member as self-initiated and denotethem by SGi,ts. Other-initiated groups OGj,ts, arethose where ai is a member of Gj,ts. As the union ofSGi,ts and those groups in OGj,ts with ai as a mem-ber may contain members of N2

i ; given gi, gj ∈ Gagents follow a preference policy Pref(gi, gj) to se-lect which team to join. The policy is formulated toensure that

1. encourage smaller groups which maximizes thenumber of groups that can execute a task

2. select for agent groups that have as many agentsfrom the first order neighborhood as possible,which increases the importance of an effectivenetwork adaptation strategy

To decide the team to join, the agent performs ad-ditional filtering and preference sorting on all of itscandidate groups based on a policy where the agentprefers

• smaller groups over larger groups

• groups most similar to its own team proposal

• groups most similar to its first order neighbor-hood

The preference for smaller teams increases the totalnumber of open positions for agents and consequentlythe total number of candidate teams. Since an agentalways proposes teams based on its first order neigh-borhood, the remaining two preferences ensure that

an agent chooses a team for which it has the maxi-mum amount of information available through its so-cial network.

The policy is defined formally as:

Pref(gi, gj) =

gi |gi| < |gj | (3)

gi |Gi ∩ gi| > |Gi ∩ gj |∧|gi| = |gj |

(4)

gi |gi ∩N1i | > |gj ∩N1

i |∧|Gi ∩ gi| = |Gi ∩ gj |∧|gi| = |gj |

(5)

gj otherwise (6)

The procedure followed by the agents in forming acollection of groups to execute a given task is sum-marized in Algorithm 1 listing.

1: procedure Select-Join-Group(Tts, A, N)2: for all i ∈ {1...N} do . iterate over agent

index3: if |Si ∩ Tts| > 0 then . run

asynchronously4: SGi,ts ←MinSetCover(N1

i , Tts)5: end if6: end for7: for all i ∈ {1...N} do8: OGi,ts ←

⋃j∈{1...N}{SGj,ts : ai ∈ SGj,ts,

9: i 6= j}10: gi,ts ← Join(SGi,ts ∪OGi,ts, P ref)11: Gts ← Gts ∪ {gi,ts}12: end for13: return Gts

14: end procedure15: procedure Join(G, ComparePolicy)16: Gsorted ← ComparisonSort(G,ComparePolicy)17: g ← Head(Gsorted) . first element of the

sorted list18: return g . discard the tail of the list19: end procedure

Algorithm 1. Agent Group Selection and Participation Algorithm

3 NETWORK ADAPTATION STRATE-GIES

Following task execution and prior to the conclusionof every time step of the simulation, agents have anoption to adapt their network connectivity. Agent aiexamines a set of agents N2

i such that ak is a memberof N2

i iff all of the following are true

• there exists an agent aj such that it is connected

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to ai via eij

• aj is connected to ak via ejk

• ak is not connected to ai via eij

• ai and ak are not the same

Intuitively, the formal description above specifies theset of all second-order neighbors (i.e. neighbors ofai’s neighbors) with exception of those that are alsoconnected to ai directly. Using the node degree ofthe agents in A, ai defines two probability mass func-tions:

P (a = ai) =1

|{A}|(7)

and

P (a = aj) =dj∑

ak∈N2i

dk(8)

Structure based network adaptation (preferen-tial attachment). By sampling from the probabil-ity density function 7, ai selects an agent aj anddeletes eij thus removing a random first order neigh-bor. Next, ai samples from probability density func-tion 8 to select agent ak and creates eik edge. Thisapproach is designed to implement the preferentialattachment policy described in [30].

Performance based network adaptation. Ourmodel also enables a complementary policy based onthe use of an agent’s local team formation perfor-mance for the network adaptation decision. Sincewe measure agent performance in terms of its effec-tiveness in joining groups and completing associatedtasks, the agent performance based network adapta-tion policy can be summarized as follows: if at timestep ts an agent ai does not select and join a team (Al-gorithm 1.), then prior to start of ts+1, ai will adaptit’s network connectivity using the preferential policyapproach described in this section. This performancepolicy is based on the expectation that if a subsetof agents AH has created a high performing networkconnectivity configuration N1

H , then their N1H should

remain static across time steps while poorly perform-ing agents should adapt their set of N1

P in an attemptto improve their performance.

Earlier research [9] [10] has addressed the question ofan appropriate strategy for selection of the candidate

agents for network adaptation as well as selection cri-teria for identifying connection destinations for thecandidate agents. There is evidence that strate-gies that enable agents to adapt connectivity basedon local structural information outperform strategieswhere agents attempt to model global network per-formance [10]. Consequently we have not attemptedto incorporate global variables (e.g. total number ofgroups formed) into individual agent decisions aboutnetwork adaptation.

IV METHOD

In the evaluation of the model, we compare impli-cations of alternative connectivity dynamics on teamformation in presence of a variable number of skillsthat every agent can contribute to a team. This sec-tion provides an overview of given related scenariosthat have been simulated as part of the study, eachscenario focusing on a unique set of network adapta-tion configurations and strategies. Each of the sce-narios has been simulated using a combination ofcommon and scenario specific sets of parameters de-scribed in Table 1. For all of the scenarios we havecollected the same set of measurements to comparethe impact of skill set diversity in team formation tostatic and preferential node attachment connectivitymodels.

The first scenario (S1 / Single Skill, No NetworkAdaptation) assumes the absence of any connectivitychanges relative to the initial, randomly created agentnetwork. To reproduce results from [10] we also re-strict the number of skills per agent with SA = 1. S1serves as a baseline to showcase average performanceof the single skill agent network across multiple simu-lations with a nontrivial sample set of possible initialrandom geometric graph configurations.

The second scenario (S2 / Single Skill, StructureBased Network Adaptation), follows [30] to reproducethe node degree based network adaptation under theSA = 1 assumption. The first step of every simula-tion under this scenario assumes random geometricgraph connectivity described in Section III.1. Priorto the beginning of the second and prior to every sub-sequent step of the simulation in this scenario, everyagent ai updates its set of edges as described in theSection III.3 on adapting network connectivity usingthe preferential policy approach.

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Name Value Description

Scenario

S1 S2 S3 S4 S5

NumSimulations 256 Number of times

each scenario has

been simulated.

NumSteps 128 Number of time

steps per sce-

nario, also num-

ber of tasks ran-

domly generated

per simulation.

N 64 Number of agents

in the simulation

scenario social

network

D 2 Manhattan dis-

tance for initial

random geomet-

ric graph agent

connectivity

such that ai is

connected to all

neighbors aj that

have Dij ≤ D|S| 16 Number of dis-

tinct skills in

the simulation

scenario

TA 8 Total number

of distinct, ran-

domly chosen

skills per task

SA 1 1 4 4 4 Total number

of distinct, ran-

domly chosen

skills per agent

Table 1. Simulation Scenario Parameters

The third scenario (S3 / Diverse Skills, No NetworkAdaptation) extends S1 through introduction of di-verse agent skill sets described earlier in this paper.No network adaptation is performed in this scenarioas it is designed to serve as an illustration of theimpact of a larger number of skills in a system onthe team candidate identification and team formationperformance.

The fourth (S4 / Diverse Skills, Performance BasedNetwork Adaptation) and fifth (S5 / Diverse Skills,Structure Based Network Adaptation) scenarios bothextend S3 using alternative network adaptationstrategies described in the section III.3. S4 uses theagent performance based network adaptation policywhile S5 relies on preferential network attachmentnetwork adaptation for every agent in the network af-ter every time step. The latter scenario’s approach isdesigned to illustrate performance of a purely randommechanism which does not incorporate considerationof the overall system performance. Introduction ofthis scenario is motivated by [10] which demonstrates

that structural policies may outperform adaptationstrategies involving agent estimation of system per-formance based on locally available information.

Since the results of the variations of the networkadaptation policy on the network structure are sim-ilar across scenarios S2, S4 and S5, they are illus-trated with the example shown on Figure 3. As aconsequence of the configuration parameters from Ta-ble 1, every agent ai is instantiated (at t = 0) withdi = 16. The figure shows that the network adap-tation policy progressively modifies the node degreedistribution towards a concentration of high degreenodes with ”fat tails” of single digit degree nodes.The degree distribution does not change significantlybeyond t = 30 to warrant additional illustrations.

Every scenario is studied through execution ofNumSimulations = 256 simulation sessions, eachsession consisting of a fixed and equal number ofsteps for all simulations. For every simulation stepwe measure the number of candidate groups identi-fied for every agent as well as the number of groupsformed during the step. In addition to tracking thedescriptive statistics (mean, standard deviation, andminimum, maximum) for these variables on per stepbasis, we also compute statistics of these variablesacross all steps in a simulation and for all of thesimulations in a scenario. The scenario scope mea-surements are needed to reduce potential bias due toselection of random geometric connectivity graphs asinitial conditions in the first step of every simulation.Simulation results are summarized in Table 2 1

Sce- Groups Formed Candidate Groups

nario µ σ M m µ σ M m

S1 0.0054 0.0731 1 0 0.0008 0.0295 3 0

S2 0.0852 0.2884 2 0 0.0216 0.1853 6 0

S3 3.1067 1.2684 8 0 0.8349 1.0439 7 0

S4 2.9661 1.2452 8 0 0.6705 1.3598 8 0

S5 2.8752 1.2012 8 0 0.6271 0.9219 8 0

Table 2. Group Formation Results

V DISCUSSION

When comparing the results for S1 and S2, we con-firm the observation that the use of agent perfor-mance based preferential node attachment policy (inS2) leads to both a higher number of groups formedand of candidate groups where the agents could par-ticipate. Compared to [30] [10] the mean values of

1The values in the table represent mean (µ), standard deviation(σ), maximum (M) and minimum (m) across allNumSimulations for a scenario.

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(a) AWD = 17.266, t=0 (b) AWD = 20.484, t=10 (c) AWD = 24.359, t=20 (d) AWD = 27.484, t=30

Fig. 3. Simulation results. Subfigures a-d show the frequency distribution of node degrees for time steps 0 through 30 along with specific values

for average weighted degree(AWD).

both variables are lower due to the difference betweenthe total number of skills in the simulations. As ar-gued by earlier research, use of structural, preferentialpolicy based network adaptation leads to significantlybetter performance in these scenarios resulting in overan order of magnitude improvement in the number ofgroups formed (from 0.0054 to 0.0852) and number ofcandidate groups per agent (from 0.0008 to 0.0216).

As argued earlier in this paper (footnote 1), intro-duction of a larger number of skills per agent can ex-ponentially increase the number of potential groupswhere the agent can participate. As shown by theresults for S3, even without any network adapta-tion, increase in skill set cardinality leads to an in-crease of approximately three orders of magnitude(from 0.0008 to 0.8349) for the mean number of thecandidate groups per agent with a parallel increase(from 0.0054 to 3.1067) in the mean number of groupsformed across the simulations in the scenario.

Given the results from research on network adapta-tion and evidence from S2, one may expect furtherimprovement to the S3 results through the introduc-tion of preferential attachment policy under the as-sumption of multiple skills per agent. However resultsof the simulation demonstrate that not to be the case.In S4, the mean number of groups formed across sim-ulations (2.9661) is not statistically significantly dif-ferent from the same number in absence of the policy,while the number of the candidate groups per agentmeasurably dropped (from 0.834846 to 0.6705). Fur-ther, S5 demonstrates that use of agent performanceinformation for network adaptation is not measurablydifferent from using a purely random preferential at-tachment policy.

Note from Figure IV that over the course of the sim-ulation, an increase of the average weighted degree(from 16 to 24.891) of the social network was less thanby a factor of two. One interpretation of this result

suggests that if the number of skills in the system |S|increases linearly while the number skills per agentSA stays constant, the preferential node attachmentnetwork adaptation policy becomes less effective asthe total space of possible task assignments growsexponentially.

VI RELATED WORK

The area of community discovery (detection) is com-plementary to our research. Community detectionwork as advanced by [36] [37] relies on a record ofpast (relative to the time of the community discov-ery query) interactions among nodes in a network.For example, by comparing frequency of edge distri-bution in a network to random edge distribution itis possible to measure modularity in a network andthus discover communities. Our research does not re-quire historical data on node interaction as we studyhow to form teams that may not have previously ex-isted as a community. However, our approach canbenefit from community discovery as history of pastinteractions can positively inform team formation.

In the solution to a TEAM FORMATION problem,Lappas et al [7] proposed to model inter-dependenciesbetween agents using an undirected, weighted so-cial graph. Edge weights in the graph can incorpo-rate measures such as effectiveness of agent-to-agentcommunication when grouping together agents intoteams. The specific algorithm in the paper finds ateam of skilled individuals which minimizes commu-nication cost among members of the team. How-ever [7] assumes a static graph structure in answeringthe team formation problem and is missing a prescrip-tive model for setting edge weights in a way indepen-dent of the application domain.

Li and Shan [15] extend [7] to account for the taskswhere some sub-tasks (a sub-problem) must be per-

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formed by a specific number of skilled individuals.Yin et al [16] extend [7] with a diversity metricbased on measurements of influence that potentialteam members receive from their peers in neighbor-ing graph nodes. The metric ensures that the teamformation solutions are biased towards having mem-bers that influence each other as little as possible.Anagnostopoulos and Becchetti [31] describe a TASKASSIGNMENT problem which seeks to ensure a bal-anced workload across team members, minimizingmaximum load over all the experts and also providean extension [14] to include communication costs sim-ilar to [7]. Kargar and An [29] point out the a mini-mum spanning tree (MST) based communication costfunction used by [7] does not effectively model teamformation scenarios where individual team membershave to communicate with each other directly. AlsoKargar and An [29] provide an alternative communi-cation cost functions that results in more stable (rel-ative to minor communications cost graph changes)solutions than those suggested by [7].

VII FUTURE WORK AND CONCLU-SIONS

The simulation-based study in this paper does notprovide a detailed, analytical treatment of the rela-tionship between the network adaptation policies andthe system-wide performance. Future research shouldfocus on further simplification of the model describedin this paper to identify the key factors negatively im-pacting scalability of the network adaptation policy.

To compare our results to [9] [10] we modeled agentskills with a uniform distribution. Future work willinclude using real world datasets [7] to bootstrap theinitial agent skill configuration.

Network adaptation outcomes may be sensitive to theinitial starting conditions in the network connectiv-ity. This study does not address this issue. In thepaper, we based the starting conditions for the net-work structure on geometric graph connectivity [30].We plan to incorporate alternative starting networkstructures from [21] to understand whether our net-work adaptation algorithms produce different resultswith scale-free or random graphs.

The implementation described in this paper relied ona simplified solver for the minimum set cover algo-rithm. Follow on work will integrate our simulationwith a production solver (e.g. CPLEX) to study themodel with larger scale data.

An increasing number of systems seek to exploit infor-mation available in Internet scale social networks toidentify teams of experts for knowledge discovery [13]or for task-oriented crowdsourcing [12]. When con-sidering performance of such systems in terms of theirability to organize groups, it is reasonable to expectthat results from studies on group formation [30] [10]should extend to more sophisticated models of in-dividual agents and their contributions to potentialgroups. Our simulation based study demonstratesthat models of agent capabilities that allow for run-time changes to agent skill sets (for example in crowd-sourcing systems like PeopleCloud [12]) introducescaling difficulties for traditional network adaptationpolicies based on preferential node attachment.

We have shown that use of more detailed skill set de-scriptions per agent (i.e. in terms of a number ofskills per agent) is desirable as it is motivated bypotential crowdsourcing applications [13] and has anet positive effect on the number of the candidategroups where an agent can contribute its skills andthe total number of groups that can be formed by asystem. However further research is needed to moreprecisely analyze and quantify the impact of preferen-tial attachment policies, and to research alternativenetwork adaptation strategies.

References

[1] P. Adler and C. Heckscher, “Collaborative Com-munity,” Ask Magazine, vol. 23, pp. 41–45, 2006.

[2] F. Bonchi, C. Castillo, and A. Gionis, “SocialNetwork Analysis and Mining for Business Ap-plications,” vol. 2, no. 3, pp. 1–37, 2011.

[3] A. Zzkarian and A. Kusiak, “Form-ing teams: an analytical approach,” IIETransactions, vol. 31, pp. 85–97, 1999,10.1023/A:1007580823003. [Online]. Available:http://dx.doi.org/10.1023/A:1007580823003

[4] E. L. Fitzpatrick and R. G. Askin, “Forming ef-fective worker teams with multi-functional skillrequirements,” Comput. Ind. Eng., vol. 48, no. 3,pp. 593–608, May 2005. [Online]. Available:http://dx.doi.org/10.1016/j.cie.2004.12.014

[5] H. Wi, S. Oh, J. Mun, and M. Jung, “Ateam formation model based on knowledge andcollaboration,” Expert Syst. Appl., vol. 36, no. 5,pp. 9121–9134, Jul. 2009. [Online]. Available:http://dx.doi.org/10.1016/j.eswa.2008.12.031

Page 11 of 13c©ASE 2012ISBN: 978-1-62561-004-1 71

[6] A. Baykasoglu, T. Dereli, and S. Das, “Projectteam selection using fuzzy optimization ap-proach,” Cybern. Syst., vol. 38, no. 2,pp. 155–185, Feb. 2007. [Online]. Available:http://dx.doi.org/10.1080/01969720601139041

[7] T. Lappas, K. Liu, and E. Terzi, “Finding ateam of experts in social networks,” Proceed-ings of the 15th ACM SIGKDD internationalconference on Knowledge discovery and datamining - KDD ’09, p. 467, 2009. [Online].Available: http://portal.acm.org/citation.cfm?doid=1557019.1557074

[8] N. Glance and B. Huberman, “Organiza-tional fluidity and sustainable cooperation,”in From Reaction to Cognition, ser. Lec-ture Notes in Computer Science, C. Castel-franchi and J.-P. MA 1

4 ller, Eds. SpringerBerlin / Heidelberg, 1995, vol. 957, pp. 89–103, 10.1007/BFb0027058. [Online]. Available:http://dx.doi.org/10.1007/BFb0027058

[9] M. Gaston and J. Simmons, “Adapting networkstructure for efficient team formation,” Proceed-ings of the AAAI 2004 Fall, 2004.

[10] M. E. Gaston and M. DesJardins, “Agent-organized networks for dynamic team forma-tion,” Proceedings of the 4th International JointConference on Autonomous Agents and Multia-gent Systems - AAMAS ’05, p. 230, 2005.

[11] K. Osipov, “AmalgaCloud: A Technical Re-port,” 2012.

[12] M. Lopez, M. Vukovic, and J. Laredo, “Peo-pleCloud Service for Enterprise Crowdsourcing,”2010 IEEE International Conference on ServicesComputing, pp. 538–545, Jul. 2010.

[13] P. Ypodimatopoulos, M. Vukovic, J. Laredo,and S. Rajagopal, “Server Hunt: Using En-terprise Social Networks for Knowledge Discov-ery in IT Inventory Management,” 2011 AnnualSRII Global Conference, pp. 418–425, Mar. 2011.

[14] A. Anagnostopoulos, L. Becchetti, C. Castillo,A. Gionis, and S. Leonardi, “Online teamformation in social networks,” in Proceedings ofthe 21st international conference on World WideWeb, ser. WWW ’12. New York, NY, USA:ACM, 2012, pp. 839–848. [Online]. Available:http://doi.acm.org/10.1145/2187836.2187950

[15] C.-T. Li and M.-K. Shan, “Team Forma-tion for Generalized Tasks in Expertise

Social Networks,” 2010 IEEE Second In-ternational Conference on Social Computing,vol. 1, pp. 9–16, Aug. 2010. [Online]. Avail-able: http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5590958

[16] H. Yin, B. Cui, and Y. Huang, “Finding a WiseGroup of Experts,” pp. 381–394, 2011.

[17] M. Kargar and A. An, “TeamExp: Top-k TeamFormation in Social Networks,” 2011 IEEE 11thInternational Conference on Data Mining Work-shops, pp. 1231–1234, Dec. 2011. [Online]. Avail-able: http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6137525

[18] B. Goncalves, N. Perra, and A. Vespignani,“Modeling users’ activity on twitter networks:validation of Dunbar’s number.” PloS one, vol. 6,no. 8, p. e22656, Jan. 2011.

[19] R. I. M. Dunbar, “The social brain hypothesis,”Evolutionary Anthropology: Issues, News, andReviews, vol. 6, no. 5, pp. 178–190, 1998.

[20] D. Schall, “Human interactions in mixedsystems-architecture, protocols, and algo-rithms,” Ph.D. dissertation, 2009. [On-line]. Available: http://www.danielschall.at/diss/DanielSchall PhDDefense.pdf

[21] R. Albert and A.-L. Barabasi, “Statisticalmechanics of complex networks,” Reviews ofModern Physics, vol. 74, no. 1, pp. 47–97, Jan. 2002. [Online]. Available: http://link.aps.org/doi/10.1103/RevModPhys.74.47

[22] M. E. J. Newman, “The structure andfunction of complex networks,” p. 58,Mar. 2003. [Online]. Available: http://arxiv.org/abs/cond-mat/0303516

[23] D. J. Watts and S. H. Strogatz, “Col-lective dynamics of ’small-world’ networks.”Nature, vol. 393, no. 6684, pp. 440–2, Jun. 1998. [Online]. Available: http://www.ncbi.nlm.nih.gov/pubmed/9623998

[24] M. E. Gaston and M. DesJardins, “Team forma-tion in complex networks,” in Proceedings of the1st NAACSOS Conference, 2003.

[25] C. Hewitt, “Offices are open systems,”ACM Trans. Inf. Syst., vol. 4, no. 3,pp. 271–287, Jul. 1986. [Online]. Available:http://doi.acm.org/10.1145/214427.214432

Page 12 of 13c©ASE 2012ISBN: 978-1-62561-004-1 72

[26] K. Sycara, S. Widoff, M. Klusch, andJ. Lu, “Larks: Dynamic matchmak-ing among heterogeneous software agentsin cyberspace,” Autonomous Agents andMulti-Agent Systems, vol. 5, no. 2, pp.173–203, Jun. 2002. [Online]. Available:http://dx.doi.org/10.1023/A:1014897210525

[27] T. L. Lenox, T. Payne, S. Hahn, M. Lewis, andK. Sycara, “Agent-based aiding for individualand team planning tasks,” in In Proceedings ofIEA 2000/HFES 2000 Congress, 2000.

[28] J. A. Giampapa and K. Sycara, “Team-OrientedAgent Coordination in the RETSINA Multi-Agent System,” Robotics Institute, CarnegieMellon University, Tech. Rep., 2002.

[29] M. Kargar and A. An, “Discovering top-kteams of experts with/without a leader insocial networks,” Proceedings of the 20th ACMinternational conference on Information andknowledge management - CIKM ’11, p. 985,2011. [Online]. Available: http://dl.acm.org/citation.cfm?doid=2063576.2063718

[30] M. Maghami and G. Sukthankar, “An agent-based simulation for investigating the impact ofstereotypes on task-oriented group formation,”in SBP’11 Proceedings of the 4th InternationalConference on Social Computing, Behavioral-cultural Modeling and Prediction, College Park,MD, USA, 2011.

[31] A. Anagnostopoulos, L. Becchetti, C. Castillo,A. Gionis, and S. Leonardi, “Power inunity: forming teams in large-scale com-munity systems,” in Proceedings of the19th ACM international conference on In-formation and knowledge management, ser.CIKM ’10. New York, NY, USA: ACM,2010, pp. 599–608. [Online]. Available:http://doi.acm.org/10.1145/1871437.1871515

[32] R. L. Rivest and C. E. Leiserson, Introduction toAlgorithms. New York, NY, USA: McGraw-Hill,Inc., 1990.

[33] R. M. Karp, Reducibility Among CombinatorialProblems. Springer Berlin Heidelberg, 2010.

[34] V. V. Vazirani, Approximation algorithms. NewYork, NY, USA: Springer-Verlag New York, Inc.,2001.

[35] H. D. Mittelmann, “Recent benchmarks of opti-mization software,” in 22nd European Confer-ence on Operational Research, Prague, CzechRepublic, 2007.

[36] B. W. Kernighan and S. Lin, “An EfficientHeuristic Procedure for Partitioning Graphs,”The Bell system technical journal, vol. 49, no. 1,pp. 291–307, 1970.

[37] M. E. J. Newman, “Modularity and communitystructure in networks.” Proceedings of the Na-tional Academy of Sciences of the United Statesof America, vol. 103, no. 23, pp. 8577–82, Jun.2006.

Page 13 of 13c©ASE 2012ISBN: 978-1-62561-004-1 73