niloy ganguly complex networks research group department of computer science & engineering...
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Niloy Ganguly
Complex Networks Research GroupDepartment of Computer Science & Engineering
Indian Institute of Technology, KharagpurKharagpur 721302
Collaborators : Sudipta Saha, Subrata Nandi, Lutz Brusch, Andreas Deutsch
Information Dissemination/Searching Large scale system
Wireless sensor network Mobile network P2P networks
Essential requirements Dissemination
o A node has an informationo Wants to spread it to all other nodes in the
network Searching
o A node wants to get some information/datao The data is somewhere in the network
Gathering (collection)
?
Data/Query packets need to cover/visit many nodes in the network
?
?
Information Dissemination/Searching
Challenge Unstructured network
o No centralized control, fully distributed
o Very large scale networko Dynamic network structureo No end to end connectivity
Constraint of Time Constraint on Energy
Main Goal : Maximize the node coverage within a given constraint of time as well as energy
Information Dissemination/SearchingFlooding, Time =2
Single RW, Time =9
General optimal algorithm for any pair of resource and time constraint
Existing algorithms Basic flooding
o Wastes a lot of resourceo Optimal in time
Single random walko Wastes a lot of timeo Optimal in resource usage
Flooding and random Walk both are optimal under a single constraint
Mutual overlap(wastage)
Overlap
Wastage of resource Visiting the same node
more than onceo Overlap with own trailo Mutual overlap
32
14
65
78
9
10
Overlap with own trail
Trail of single walker
Node / site
Start
Overlap
Wastage of resource Visiting the same node
more than onceo Overlap with own trailo Mutual overlap
Mutual Overlap
Trail of walker 1
Node / site
Trail of walker 2
Start
Start
Understanding the Problem Space Three broad regions
Time
Ban
dwid
th
Building Proliferation Strategy
• Walkers originate from a single point like flooding and random walk
• Walkers multiply at certain rate (say) P- proliferation rate
• For each point in the graph, a P would be needed – determining best P for each point
Optimal Proliferation Rate
• Proliferation Rate which enhances speed but does not cause mutual overlap like single random walker
• Each walker has its own area (although new walkers are produced from old walkers)
K-RW - The statistical mechanics perspective
Regime I Regime II Regime III
Results on d – dimensional grid Euclidean dimension (Larralde et. al. ‚02)
Ref: H. Larralde, P. Turnfio, S. Havlin, H. E. Stanley and G. H. Weiss, Nature, 355:423 - 426, 2002.
Increase in coverage
Observations and Inference
1. In regime I, coverage rate is similar to flooding.
2. In regime II, walkers move far apart each other and less walkersco-occupy nodes. However, still some amount of mutual overlap persists.
3. In regime III, each walker behaves independently like a singlerandom walker with non-overlapping exploration space, covers with peak efficiency Emax=E1-RW.
Regime I Regime II Regime III
Proposed Algorithm
Start with a small number of random walkers at t = 1
Proliferating each walker at a suitable rate P*(t) at each time step,
Aim :- System always remains at the regime boundary (II- III) as desired.
• Bandwidth consumed
• Lower bound of time to achieve Cmax,
• Speed-up
Speed-up vis-à-vis 1-RW
Contribution
Coverage maximization in networks under resource constraints, Subrata Nandi, Lutz Brusch, Andreas Deutsch and Niloy Ganguly, Phys. Rev. E 81, 061124 (2010)
• We develop a coverage algorithm P*(t)-RW with proliferating message packets and temporally modulated proliferation rate.
• Proliferation -- a walker self-replicates at its current node with rate P*(t) Є R+ at time t such that on average each walker produces one offspring walker every 1/P*(t) time steps
• The algorithm performs as efficiently as 1-RW, covers Cmax but (B (d−2)/d) times faster, resulting in significant service speed-up on a regular grid of dimension d.
Contribution
Time (T)
Reso
urc
e (
B)
Coverage maximization in networks under resource constraints, Subrata Nandi, Lutz Brusch, Andreas Deutsch and Niloy Ganguly, Phys. Rev. E 81, 061124 (2010)
The Problem Space
Time (t)
Reso
urc
e
(B)
We need optimal strategy for Zone 2 and in general for any given (B,T) pair
Phase diagram – explains the problem space
Our Study
Standard deviation of mutual overlap in proliferating random Walk
Average mutual overlap in proliferating random walk
Is heterogeneity better from the perspective of coverage under
bounded resource?*\alpha = 1 optimal strategy
Our Study
Standard deviation of mutual overlap in K-random walk
Average mutual overlap in K - random walk
Strategy
Reduce Heterogeneity or
Increase Heterogeneity
Our Study
Relationship between concentration of the walkers and their mutual overlap
o Two distinct phaseso Phase I - low mutual
overlap, very short, highly sensitive to the concentration
o Phase II - High mutual overlap, Insensitive to concentration
Main Challenge
Hence, the more walkers an algorithm can keep in Phase I, the more utilization of the resource and time, it can make
Main Challenge
More walkers in Phase 1
(low density)
Proliferate only when a walker is in a very sparse region
Our Strategy Calculate local density of an walker
A difficult task without centralized control
Our solution - replaces the spatial measurement of the density with the temporal measuremento Walkers record how many of its previous
visits are mutual overlap
This approximation of density correlates with actual density Temporal measure
Spati
al m
easu
re
Correlation is better for higher proliferation
rates
Our Strategy We made proliferation rate proportional to this temporal density
e.g., p(t) is the per walker proliferation rate, we replace α by αh
Coverage maximization under resource constraints using non-uniform proliferating random walk, Sudipta Saha and Niloy Ganguly, Phys. Rev. E 87, 022807 (2013)
γ=0 ; The strategy is equivalent to base strategy
γ>0 ; As γ increases, we proliferate more those walkers which face lesser mutual overlap in last H visits
Observation: γ=20 and above gives maximum improvement o Only zero mutual overlaps are
proliferated
Rate of proliferation is now inversely proportional to the number of mutual overlap a walker has faced
Proliferating only at zero mutual overlap – produced maximum efficiency
Improvements – In 2D regular grid 250% In 3D regular grid 133% In 4D regular grid 80% In 5D regular grid 20% In 2D random geometric graph
233%
We proliferated only those walkers which faced zero mutual overlap in the last H node visits (identified as Phase-I walkers)
This strategy is denoted by P(t,h)-RW-e and performed extremely well in comparison with other existing strategies
Our Strategy
Coverage maximization under resource constraints using non-uniform proliferating random walk, Sudipta Saha and Niloy Ganguly, Phys. Rev. E 87, 022807 (2013)
Conclusion
Solution for the entire space
Significant Performance Improvement
Time (T)
Reso
urc
e (
B)
Resou
rce
(B)
Covera
ge
(C)
Z
X
Y
Time (T)
New Problem Definition
Optimize with Knowledge
Maximize the functionC=f(B,T, K)
Knowledge
Complex Network
Research group (CNeRG)
28
Coverage maximization in networks under resource constraints, Subrata Nandi, Lutz Brusch, Andreas Deutsch and Niloy Ganguly, Phys. Rev. E 81, 061124 (2010)
maximization under resource constraints using non-uniform proliferating random walk, Sudipta Saha and Niloy Ganguly, Phys. Rev. E 87, 022807 (2013)
Thank You
Conclusion
Time (t)
Reso
urc
e
(B)
Effect of History Size
“Coverage maximization under resource constraints using non-uniform proliferating random walk”
Sudipta Saha and Niloy Ganguly, Phys. Rev. E 87, 022807 (2013)
History size has significant effect on the performance of the strategy also
Lower history size may not identify the proper phase 1 walkers
Higher history size may proliferate less frequently than what is required
If both 0 and 1 overlaps are proliferatedo For higher history size
they behave almost equally
Optimal history size depends on topology as well as walker forwarding policy
A Different Perspective Key observations
In regular grid – as dimension increases, the random walk strategy becomes more efficient
A random walker travels more distance on average from the start node as dimension increases
A walker in the developed history based strategy travels the maximum distance from the start node in comparison to other existing algorithms
Efficiency of the strategyThe average distance a walker can travel from the start node
Is Correlated
?
Challenges Finding out unique and optimal
directiono For static network – it is outwards the center
node o But needs the information of the position of
the centero For dynamic networks it is more difficult
Finding out the balancing proliferation rate
A Different Perspective
θ
Forwarded with higher bias to this node
New strategy Walker should move in such a way that they can
travel maximum distance from the start node on average Should move along a direction
They should follow unique direction to minimize mutual overlap A
A Different Perspective Alternative way (a possible bio-inspired strategy)
We can learn from the spreading mechanism of cancer cells Density biased proliferating random walk
o We approximate spatial density by temporal densityo If we an approximate spatial density itselfo How exactly the cancer cells estimates density in a distributed fashiono Can be implemented using artificial pheromone
At what rate they proliferate ?
How cancer cells migrate from one place to another? How they sense
density ?
Do they optimize food resource and time?
?
