Hop limited flooding over dynamic networks

We study the performance of hop-limited broadcasting of a message in dynamic graphs where links between nodes switch between active and inactive states. We analyze the performance with respect to the completion time, defined as the time for the message to reach a given portion of nodes, and the communication complexity, defined as the number of message forwarding per node. We analyze two natural flooding algorithms. First is a lazy algorithm where the message can be forwarded by a node only if it was first received by this node through a path shorter than the hop limit count. Second is a more complex protocol where each node forwards the message at a given time, if it could have been received by this node through a path shorter than the hop limit count. We derive exact asymptotics for the completion time and the communication complexity for large network size which reveal the effect of the hop limit count. Perhaps surprisingly, we find that both flooding algorithms perform near optimum and that the simpler (lazy) algorithm is only slightly worse than the other, more complicated algorithm. The results provide insights into performance of networked systems that use hop limits, for example, in the contexts of peer-to-peer systems and mobile ad-hoc networks.

[1]  Adam Shwartz,et al.  Large Deviations For Performance Analysis , 2019 .

[2]  Laurent Massoulié,et al.  The diameter of opportunistic mobile networks , 2007, CoNEXT '07.

[3]  Peter Neal,et al.  The Generalised Coupon Collector Problem , 2008, Journal of Applied Probability.

[4]  Ness B. Shroff,et al.  Delay and Capacity Trade-Offs in Mobile Ad Hoc Networks: A Global Perspective , 2006, Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications.

[5]  Jean-Yves Le Boudec,et al.  The age of gossip: spatial mean field regime , 2009, SIGMETRICS '09.

[6]  Juraj Hromkovič,et al.  Dissemination of Information in Interconnection Networks (Broadcasting & Gossiping) , 1996 .

[7]  Doug Terry,et al.  Epidemic algorithms for replicated database maintenance , 1988, OPSR.

[8]  Andrea E. F. Clementi,et al.  Flooding time in edge-Markovian dynamic graphs , 2008, PODC '08.

[9]  Joseph Y. Halpern,et al.  Gossip-based ad hoc routing , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[10]  Rajeev Motwani,et al.  Randomized Algorithms , 1995, SIGA.

[11]  David Tse,et al.  Mobility increases the capacity of ad hoc wireless networks , 2002, TNET.

[12]  Yu-Chee Tseng,et al.  The Broadcast Storm Problem in a Mobile Ad Hoc Network , 1999, Wirel. Networks.

[13]  Jean-Yves Le Boudec,et al.  Self-Limiting Epidemic Forwarding , 2006 .

[14]  Pan Hui,et al.  BUBBLE Rap: Social-Based Forwarding in Delay-Tolerant Networks , 2008, IEEE Transactions on Mobile Computing.

[15]  D. Du,et al.  Combinatorial Network Theory , 1996 .

[16]  Roger Wattenhofer,et al.  Information dissemination in highly dynamic graphs , 2005, DIALM-POMC '05.

[17]  Rajesh Sundaresan,et al.  Delay and energy optimal two-hop relaying in delay tolerant networks , 2010, 8th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks.

[18]  Alexander M. Haimovich,et al.  Decentralized two-hop opportunistic relaying with limited channel state information , 2008, 2008 IEEE International Symposium on Information Theory.

[19]  Richard M. Karp,et al.  Randomized rumor spreading , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[20]  Andrea E. F. Clementi,et al.  Broadcasting in dynamic radio networks , 2009, J. Comput. Syst. Sci..

[21]  Nancy A. Lynch,et al.  Distributed computation in dynamic networks , 2010, STOC '10.

[22]  Patrick Stuedi,et al.  The Duality between Message Routing and Epidemic Data Replication , 2009, HotNets.

[23]  Hung-Yu Wei,et al.  Two-hop-relay architecture for next-generation WWAN/WLAN integration , 2004, IEEE Wireless Communications.

[24]  Pierre Fraigniaud,et al.  Parsimonious flooding in dynamic graphs , 2009, PODC '09.

[25]  B. Pittel.  On spreading a rumor , 1987 .