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Optimal Channel Choice for Collaborative Ad-Hoc Dissemination. Liang Hu Technical University of Denmark. Jean -Yves Le Boudec EPFL. Milan Vojnović Microsoft Research. IEEE Infocom 2010, San Diego , CA, March 2010.

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Optimal Channel Choice for Collaborative Ad-Hoc Dissemination

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## Optimal Channel Choice for Collaborative Ad-Hoc Dissemination

Liang Hu

Technical University of Denmark

Jean-Yves Le Boudec

EPFL

Milan Vojnović

Microsoft Research

IEEE Infocom 2010, San Diego, CA, March 2010

channels

users

infrastructure

### Outlook

• System welfare objective

• Optimal GREEDY algorithm for solving the system welfare problem

• Distributed Metropolis-Hastings algorithm

• Simulation results

• Conclusion

### Assignment of channels to users for dissemination

• User u subscribed to a set of channels S(u)

• xuj = 1 if user forwards channel j, xuj = 0 otherwise

• Constraint: each user u forwards at most Cu channels

u

j

users

channels

• Find:an assignment of users to channels that maximizes a system welfare objective

### System Welfare Problem

= dissemination time for channel j under assignment x

### System Welfare Problem (cont’d)

• In this paper we consider the problem under assumptionfor every channel ji.e. utility of channel j is a function of the fraction of users that forward channel j

• For example, the assumption holds under random mixing mobility where each pair of nodes is in contact at some common positive rate

### Dissemination Time for Random Mixing Mobility

Access rate at which channel j

the infrastructure

Fraction of subscribers of

channel j

Fraction of subscribers of

message by time t

Fraction of forwarders of

message by time t

Fraction of forwarders of

channel j

Time for the message to reach a fraction of subscribers:

### Dissemination Time ... (cont’d)

Also observed in real-world mobility traces (Cambridge dataset):

• Polyhedron:

• where

### System Welfare Problem (cont’d)

• Proof sketch: max-flowmin-cut arguments

• For every subset of channels A: = flowv(A) = min-cut

• max-flowachieved by an integral assignment

user u subscribed to this channel

0



Cu - |S(u)|



s

1

t

j

u



users

channels

### Outlook

• System welfare objective

• Optimal GREEDY algorithm for solving the system welfare problem

• Distributed Metropolis-Hastings algorithm

• Simulation results

• Conclusion

### GREEDY

Init:Hj = 0 for every channel j

while 1 doFind a channelJfor which incrementing HJ by one (if feasible) increases the systemwelfare themostif no such J exists then breakHJ ← HJ + 1

end while

### GREEDY is Optimal

• Proof sketch: - objective function is concave- polyhedron is submodularvalidating the conditions for optimality of the greedy procedure (Federgruen & Groenevelt, 1986)

Uj(t)

Uj(t)

- 

dj

t

dj

t

### Outlook

• System welfare objective

• Optimal GREEDY algorithm for solving the system welfare problem

• Distributed Metropolis-Hastings algorithm

• Simulation results

• Conclusion

### Distributed Algorithm

• Metropolis-Hastings sampling

• Choose a candidate assignment x’ with prob. Q(x, x’) where x is the current assignment

• Switch to x’ with prob. where

An example local rewiringwhen users u and v in contact:

u

v

User u samples a candidate

assignment where user u switched to forwarding a randomly picked

channel forwarded by user v

- Requires knowing fractions fj (can be estimated locally)

temperature

normalization constant

### User’s Battery Level

• The system welfare objective extended to

• Additional factor for the acceptance probabilityfor our example rewiring:

Wu,j(b)

battery level for user u

b

### Simulation Results

• Cambridge mobility trace

• Vj(f) = - tj(f) for every channel j

• J = 40 channels, 20 channels fwd per user, 10 subs. per user

• Subscriptions per channel ~ Zipf(2/3)

Dissemination time per channel in minutes

UNI = pick a channel to help uniformly at random

TOP = pick a channel to help in

decreasing order of channel

popularity

### Conclusion

• Formulated a system welfare objective for optimizing dissemination of multiple information streams

• For cases where the dissemination time of a channel is a function of the fraction of forwarders

• Showed that the problem is a concave optimization problem that can be solved by a greedy algorithm

• Distributed algorithm via Metropolis-Hastings sampling

• Simulations confirm benefits over heuristic approaches

• Future work – optimizing a system welfare objective under general user mobility?