distributed graph transformations supported by multi-agent systems
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DISTRIBUTED GRAPH TRANSFORMATIONS
SUPPORTED BY MULTI-AGENT SYSTEMS
Adam Sędziwy, PhDAGH University of Science and
Technology Cracow, Poland
1. Objectives2. Graph transformations. The
complexity3. Faciliating graph transformations4. The role of an agent system5. Case study6. Examples of applications7. Summary
OUTLINE
Graph models are widely used for describing a range of systems. For that reason we focus on:
Developing the eff ective method of graph-based computations
Computations have to be performed in parallel
Computations are intended to be carried out by an agent system
OBJECTIVES
A graph grammar is a generalization of a string grammar notion:
The example:
Terminal and nonterminal symbols are replaced by terminal and nonterminal vertices (context-free grammar) or graphs (context grammar)
GRAPH GRAMMARS
The sample graph production:
Q: how to embed R in G-X ? A: Embedding rule is associated with each production.1. Edges {i,X} where i≠a , should be removed2. The (former) edge {a,X} should be replaced with {a,Y} and
{a,e}
GRAPH GRAMMARS (CONT.)
The basic problem: exponential complexity of parsing and membership problem
A graph grammar's parsing complexity vs expressiveness
If some restrictions are imposed on a grammar then the complexity reduction is possible (edNLC, ETPL(k), … )
COMPLEXITY ISSUES
A graph should be decomposed into complementary subgraphs. – Q: How?– A: It depends on a problem: equally sized subgraphs, minimized number of connections, minimized redundancy,...
Processing is performed in parallel with some data exchange.
The desirable property: centralized graph grammar rules apply to be used in a distributed environment
FACILITATING GRAPH COMPUTATIONS –
"WHAT IS TO BE DONE”?
Decomposition based on a vertex replication
GRAPH DECOMPOSITION – VERTEX REPLICATION
Motivation: applicable to subproblems requiring an autonomous activity (decision making) rather than executing a deterministic algorithm
Particular subtasks (e.g., local graph transformations) are performed by agents
An agent's knowledge is represented by a graph structure (data) and a grammar (action)
Agents have to cooperate to achieve their goals
AGENT SYSTEM ON A DISTRIBUTED GRAPH
Centralized graph decomposition
The scenario of a local production
A node’s incorporation
Confl icts
CASE STUDY
The graph G in a centralized and ditributed form
CASE STUDY - DECOMPOSITION
The agent A1 aims at applying the production P to G1
A1 has to obtain an exclusive access to the vertex v
CASE STUDY – THE LOCAL PRODUCTION
Replicas of v have to be removed from other subgraphs incorporation of the vertex v to G1
To preserve the overall consistency the agent A1 requests other agentsto lock relevant vertices (e.g., u,w) while incoroprating v
The source of confl icts!
CASE STUDY - INCORPORATION
A1 determines a set HA (L) of other agents hosting vertices of L
A1 follows 2PC:PHASE 1: A1 requests agents A iHA(L) to block vertices of L
A i responds with AGREEMENT=YES | NO:BLOCKED | NO:NONEXIST
PHASE 2: [AGREEMENT=YES] A1 sends COMMIT; A i responds with a
relevant part of L [AGREEMENT=NO:BLOCKED] A1 sends ABORT to HA(L) and
restarts with a random delay [AGREEMENT=NO:NONEXIST] A1 sends ABORT to HA(L) and
tries to determine HA(L) again
CASE STUDY – INCOROPRATION (CONT.)
CASE STUDY – INCOROPRATION (CONT.)
The agent A1 has incorporated the vertex v
Embedding rules: {p,q} is replaced by {p,a} {p,r} is replaced by {p,b} {u,v} is replaced by {u,a} {w,v} is replaced by {w,b} {q,v}, {r,v} are removed
CASE STUDY - PRODUCTION
P
A border node v may be shared by all complementary graphs (pessimistic case), i.e., O(N).
Pessimistically, the number of vertices to be locked is:
The additional issue: a number of exchanged messages
Solution: the another approach to the graph decomposition – the graph slashing
CONFLICTS
Slashed graphs concept. A single edge is shared by exactly two agents
GRAPH DECOMPOSITION – SLASHING
𝑛𝐿=𝑂 (𝑑𝑚𝑎𝑥 )
CAD system for the architectural design
Separate design processes and graph models for the interior and exterior
Both processes may clash on shared elements (e.g., windows): coordination required
EXAMPLE 1
The control in smart lighting systems
The lighting control is based on sensor data (reflecting an environment state)
Lamps’ performance is controlled by relevant graph grammar productions triggered by changes in an environment
EXAMPLE 2
The graph-based representation (GBR) of systems is the suitable formal approach to model a range of systems.
GBR may be easily decomposed becoming an environment for an agent system deployment
A decomposition method depends on a problem. Following factors should be considered: Statistical properties of an agent system’s behavior
(avoiding conflicts) A number of messages required for completing atomic
operations
SUMMARY
1. L. Kotulski, A. Sędziwy, B. Strug: Heterogeneous graph grammars synchronization in CAD systems supported by hypergraph representations of buildings , Expert Systems with Applications, Elsevier, http://dx.doi.org/10.1016/j.eswa.2013.07.043
2. I. Wojnicki, S. Ernst, L. Kotulski, A. Sędziwy: Advanced Street Lighting Control , Expert Systems with Applications, Elsevier, http://dx.doi.org/10.1016/j.eswa.2013.07.044
3. A. Sędziwy: Eff ective Graph Representation for Agent-Based Distributed Computing , Lecture Notes in Computer Science, Vol. 7327, pp 638-647, Springer, 2012
4. L. Kotulski, A. Sędziwy: Parallel graph transformations supported by replicated complementary graphs , Lecture Notes in Computer Science, Vol. 6594, pp 254-264, Springer, 2011
FOR FURTHER READING
THANK YOU FOR YOUR ATTENTION
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