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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 O(log2 n) and network diameter of O(log2 n), or (b) have a routing table of size(More)
A number of Distributed Hash Table (DHT)-based protocols have been proposed to address the issue of scalability in peer-topeer 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, we(More)
We study the problem of covering graphs with trees and a graph of bounded maximum degree. By a classical theorem of Nash-Williams, every planar graph can be covered by three trees. We show that every planar graph can be covered by two trees and a forest, and the maximum degree of the forest is at most 8. Stronger results are obtained for some special(More)
Motivated by a multi-tree approach to the design of reliable communication protocols, Itai and Rodeh gave a linear time algorithm for finding two independent spanning trees in a 2-connected graph. Cheriyan and Maheshwari gave an O(|V |) algorithm for finding three independent spanning trees in a 3-connected graph. In this paper we present an O(|V |)(More)
Let G be a graph, {a, b, c} ⊆ V (G), and {a, b, c} ⊆ V (G) such that {a, b, c} 6= {a, b, c}. We say that (G, {a, c}, {a, c}, (b, b)) is an obstruction if, for any three vertex disjoint paths from {a, b, c} to {a, b, c} in G, one path is from b to b. In this paper we characterize obstructions. ∗Partially supported by NSF grant DMS-9970527 and NSA grant(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)
Let G be a graph and u, v be two distinct vertices of G. A u−v path P is called nonseparating if G − V (P ) is connected. The purpose of this paper is to study the number of nonseparating u− v path for two arbitrary vertices u and v of a given graph. For a positive integer k, we will show that there is a minimum integer α(k) so that if G is an(More)