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— In this work, we study a fundamental tradeoff issue in designing distributed hash table (DHT) in peer-to-peer networks: the size of the routing table v.s. the network diameter. It was observed by Ratnasamy et al. that existing DHT schemes either (a) have a routing table of size Ç´ÐÓÓ ¾ Òµ and network diameter of Ç´ÐÓÓ ¾ Òµ, or (b) have a routing table of(More)
The circumference of a graph is the length of its longest cycles. Results of Jackson, and Jackson and Wormald, imply that the circumference of a 3-connected cubic n-vertex graph is Ω(n 0.694), and the circumference of a 3-connected claw-free graph is Ω(n 0.121). We generalise and improve the first result by showing that every 3-edge-connected graph with m(More)
— A number of Distributed Hash Table (DHT)-based protocols have been proposed to address the issue of scalability in peer-to-peer networks. However, it remains an open question whether there exists a DHT scheme that can achieve the theoretical lower bound of on network diameter when the average routing table size at nodes is no more than¨©. In this paper,(More)
A graph is subcubic if its maximum degree is at most 3. The bipartite density of a graph G is max{ε(H)/ε(G) : H is a bipartite subgraph of G}, where ε(H) and ε(G) denote the numbers of edges in H and G, respectively. It is an NP-hard problem to determine the bipartite density of any given triangle-free cubic graph. Bondy and Locke gave a polynomial time(More)
The class of graphs with no K3,t-minors, t ≥ 3, contains all planar graphs and plays an important role in graph minor theory. In 1992, Seymour and Thomas conjectured the existence of a function α(t) > 0 and a constant β > 0, such that every 3-connected n-vertex graph with no K 3,t-minors, t ≥ 3, contains a cycle of length at least α(t)n β. The purpose of(More)