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.

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Optimal Channel Choice for Collaborative Ad-Hoc Dissemination

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Optimal channel choice for collaborative ad hoc dissemination

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


Delivery of information streams through the infrastructure and device to device transfers

Delivery of Information Streamsthrough the infrastructure and device-to-device transfers

channels

users

infrastructure


Outlook

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

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

System Welfare Problem

= dissemination time for channel j under assignment x


System welfare problem cont d

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


System welfare problem cont d1

System Welfare Problem (cont’d)


Dissemination time for random mixing mobility

Dissemination Time for Random Mixing Mobility

Access rate at which channel j

content is downloaded from

the infrastructure

Fraction of subscribers of

channel j

Fraction of subscribers of

channel j that received the

message by time t

Fraction of forwarders of

channel j that received the

message by time t

Fraction of forwarders of

channel j

Time for the message to reach a fraction of subscribers:


Dissemination time cont d

Dissemination Time ... (cont’d)

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


System welfare problem cont d2

System Welfare Problem (cont’d)

  • Polyhedron:

  • where


System welfare problem cont d3

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


Outlook1

Outlook

  • System welfare objective

  • Optimal GREEDY algorithm for solving the system welfare problem

  • Distributed Metropolis-Hastings algorithm

  • Simulation results

  • Conclusion


Greedy

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

GREEDY is Optimal

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


When v j f is concave

When Vj(f) is concave?

Uj(t)

Uj(t)

- 

dj

t

dj

t


Outlook2

Outlook

  • System welfare objective

  • Optimal GREEDY algorithm for solving the system welfare problem

  • Distributed Metropolis-Hastings algorithm

  • Simulation results

  • Conclusion


Distributed algorithm

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

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

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

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?


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