Modeling and Analysis of Time-Varying Graphs

We live in a world increasingly dominated by networks -- communications, social, information, biological etc. A central attribute of many of these networks is that they are dynamic, that is, they exhibit structural changes over time. While the practice of dynamic networks has proliferated, we lag behind in the fundamental, mathematical understanding of network dynamism. Existing research on time-varying graphs ranges from preliminary algorithmic studies (e.g., Ferreira's work on evolving graphs) to analysis of specific properties such as flooding time in dynamic random graphs. A popular model for studying dynamic graphs is a sequence of graphs arranged by increasing snapshots of time. In this paper, we study the fundamental property of reachability in a time-varying graph over time and characterize the latency with respect to two metrics, namely store-or-advance latency and cut-through latency. Instead of expected value analysis, we concentrate on characterizing the exact probability distribution of routing latency along a randomly intermittent path in two popular dynamic random graph models. Using this analysis, we characterize the loss of accuracy (in a probabilistic setting) between multiple temporal graph models, ranging from one that preserves all the temporal ordering information for the purpose of computing temporal graph properties to one that collapses various snapshots into one graph (an operation called smashing), with multiple intermediate variants. We also show how some other traditional graph theoretic properties can be extended to the temporal domain. Finally, we propose algorithms for controlling the progress of a packet in single-copy adaptive routing schemes in various dynamic random graphs.

[1]  Rabin K. Patra,et al.  Routing in a delay tolerant network , 2004, SIGCOMM '04.

[2]  Tim Roughgarden,et al.  Single-Source Stochastic Routing , 2006, APPROX-RANDOM.

[3]  Pan Hui,et al.  Pocket Switched Networking: Challenges, Feasibility and Implementation Issues , 2005, WAC.

[4]  Arun Venkataramani,et al.  DTN routing as a resource allocation problem , 2007, SIGCOMM '07.

[5]  Jukka-Pekka Onnela,et al.  Community Structure in Time-Dependent, Multiscale, and Multiplex Networks , 2009, Science.

[6]  Afonso Ferreira,et al.  Building a reference combinatorial model for MANETs , 2004, IEEE Network.

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

[8]  Prithwish Basu,et al.  Opportunistic forwarding in wireless networks with duty cycling , 2008, CHANTS '08.

[9]  Saikat Guha,et al.  Effect of limited topology knowledge on opportunistic forwarding in ad hoc wireless networks , 2010, 8th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks.

[10]  Mostafa Ammar,et al.  Routing in Space and Time in Networks with Predictable Mobility , 2004 .

[11]  Dimitri P. Bertsekas,et al.  Data Networks , 1986 .

[12]  Prithwish Basu,et al.  Exact Analysis of Latency of Stateless Opportunistic Forwarding , 2009, IEEE INFOCOM 2009.

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

[14]  Cecilia Mascolo,et al.  Temporal distance metrics for social network analysis , 2009, WOSN '09.

[15]  Binoy Ravindran,et al.  On Distributed Time-Dependent Shortest Paths over Duty-Cycled Wireless Sensor Networks , 2010, 2010 Proceedings IEEE INFOCOM.

[16]  Baruch Schieber,et al.  The Canadian Traveller Problem , 1991, SODA '91.

[17]  Andrea E. F. Clementi,et al.  Communication in dynamic radio networks , 2007, PODC '07.

[18]  Ram Ramanathan,et al.  Challenges: a radically new architecture for next generation mobile ad hoc networks , 2005, MobiCom '05.

[19]  Giuseppe F. Italiano,et al.  Experimental analysis of dynamic all pairs shortest path algorithms , 2004, SODA '04.

[20]  Andréa W. Richa,et al.  Finding Most Sustainable Paths in Networks with Time-Dependent Edge Reliabilities , 2002, LATIN.