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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.

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Optimal Channel Choice for Collaborative Ad-Hoc Dissemination

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  1. 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

  2. Delivery of Information Streamsthrough the infrastructure and device-to-device transfers channels users infrastructure

  3. Outlook • System welfare objective • Optimal GREEDY algorithm for solving the system welfare problem • Distributed Metropolis-Hastings algorithm • Simulation results • Conclusion

  4. 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

  5. System Welfare Problem = dissemination time for channel j under assignment x

  6. System Welfare Problem (cont’d) • In this paper we consider the problem under assumption for 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

  7. System Welfare Problem (cont’d)

  8. 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:

  9. Dissemination Time ... (cont’d) Also observed in real-world mobility traces (Cambridge dataset):

  10. System Welfare Problem (cont’d) • Polyhedron: • where

  11. 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

  12. Outlook • System welfare objective • Optimal GREEDY algorithm for solving the system welfare problem • Distributed Metropolis-Hastings algorithm • Simulation results • Conclusion

  13. 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

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

  15. When Vj(f) is concave? Uj(t) Uj(t) -  dj t dj t

  16. Outlook • System welfare objective • Optimal GREEDY algorithm for solving the system welfare problem • Distributed Metropolis-Hastings algorithm • Simulation results • Conclusion

  17. 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

  18. 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

  19. 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

  20. 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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