TY - GEN

T1 - Radio cover time in hyper-graphs

AU - Avin, Chen

AU - Lando, Yuval

AU - Lotker, Zvi

PY - 2010

Y1 - 2010

N2 - In recent years, protocols that are based on the properties of random walks on graphs have found many applications in communication and information networks, such as wireless networks, peer-to-peer networks, and the Web. For wireless networks, graphs are actually not the correct model of the communication; instead, hyper-graphs better capture the communication over a wireless shared channel. Motivated by this example, we study in this paper random walks on hyper-graphs. First, we formalize the random walk process on hyper-graphs and generalize key notions from random walks on graphs. We then give the novel definition of radio cover time, namely, the expected time of a random walk to be heard (as opposed to visited) by all nodes. We then provide some basic bounds on the radio cover, in particular, we show that while on graphs the radio cover time is O(mn), in hyper-graphs it is O(mnr), where n, m, and r are the number of nodes, the number of edges, and the rank of the hyper-graph, respectively. We conclude the paper with results on specific hyper-graphs that model wireless mesh networks in one and two dimensions and show that in both cases the radio cover time can be significantly faster than the standard cover time. In the two-dimension case, the radio cover time becomes sub-linear for an average degree larger than log2 n.

AB - In recent years, protocols that are based on the properties of random walks on graphs have found many applications in communication and information networks, such as wireless networks, peer-to-peer networks, and the Web. For wireless networks, graphs are actually not the correct model of the communication; instead, hyper-graphs better capture the communication over a wireless shared channel. Motivated by this example, we study in this paper random walks on hyper-graphs. First, we formalize the random walk process on hyper-graphs and generalize key notions from random walks on graphs. We then give the novel definition of radio cover time, namely, the expected time of a random walk to be heard (as opposed to visited) by all nodes. We then provide some basic bounds on the radio cover, in particular, we show that while on graphs the radio cover time is O(mn), in hyper-graphs it is O(mnr), where n, m, and r are the number of nodes, the number of edges, and the rank of the hyper-graph, respectively. We conclude the paper with results on specific hyper-graphs that model wireless mesh networks in one and two dimensions and show that in both cases the radio cover time can be significantly faster than the standard cover time. In the two-dimension case, the radio cover time becomes sub-linear for an average degree larger than log2 n.

KW - cover time

KW - distributed algorithms

KW - hitting time

KW - hyper-graphs

KW - random walks

KW - wireless networks

UR - http://www.scopus.com/inward/record.url?scp=78549286067&partnerID=8YFLogxK

U2 - 10.1145/1860684.1860689

DO - 10.1145/1860684.1860689

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AN - SCOPUS:78549286067

SN - 9781450304139

T3 - Proceedings of the 6th International Workshop on Foundations of Mobile Computing, DIALM-POMC '10

SP - 3

EP - 12

BT - Proceedings of the 6th International Workshop on Foundations of Mobile Computing, DIALM-POMC '10

T2 - 6th ACM SIGACT-SIGMOBILE International Workshop on Foundations of Mobile Computing, DIALM-POMC 2010

Y2 - 16 September 2010 through 16 September 2010

ER -