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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)
iii ACKNOWLEDGEMENTS My thesis advisor, Professor Ye (Geoffrey) Li, has my sincerest gratitude for having taught me so much about doing research. It was his insight that helped me to initiate this topic. This thesis has significantly benefited from his valuable guidance and constant encouragement. I also greatly appreciate his care and concern for my(More)
We study the existence of certain disjoint paths in planar graphs and generalize a theorem of Thomassen on planarizing cycles in surfaces. Results are used to prove that every 5-connected triangulation of a surface with sufficiently large representativity is hamiltonian, thus verifying a conjecture of Thomassen. We also obtain results about spanning walks(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)
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 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)