Multicasting in the Hypercube, Chord and Binomial Graphs

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Multicasting in the Hypercube, Chord and Binomial Graphs (2009)

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by Christopher C. Cipriano , Teofilo F. Gonzalez

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51	Unlikelihood that minimal phylogenies for a realistic biological study can be constructed in reasonable computational time. Mathematical Biosciences 60:133–142 - Graham, Foulds - 1982 (Show Context) Citation Context ... problem with the added constraint dT(u0, ui) = dG(u0, ui) for 1 ≤ i ≤ k, where dT(a, b) and dG(a, b) is the number of edges in a shortest path from a to b in T and G, respectively. Graham and Foulds =-=[1]-=- studied the MST problem for the n-cube in order to determine the possibility of computing specific biological sciences problems in reasonable time. Their work resulted in a complex proof for the NP-C...
33	Optimal routing in Chord - Ganesan, Manku - 2004 (Show Context) Citation Context ...o implement optimum unicasting (multicasting to one destination) in the n-cube. Optimal polynomial time algorithms for unicasting have been developed for both the Chord and the binomial graph network =-=[4, 3]-=-; however, there has not been a lot of work on multicasting in these topologies. It was conjectured that optimum sp-multicast trees for the binomial graph network can be constructed by simply using th...
5	Optimal Communication Trees with Application to Hypercube Multiprocessors,” Graph Theory - Choi, Esfahanian, et al. - 1991 (Show Context) Citation Context ...ness of the decision version of the Steiner tree problem for the n-cube. Later on, a complex transformation and proof was used to establish that the sp-multicast problem for the n-cube is NP-Complete =-=[2, 3]-=-. In this paper we present simple transformations and proofs that establish the NP-Completeness of these two problems. An n-cube (hypercube) consists of 2n vertices or processors. Every vertex in the ...
4	On Complexity of a Message-Routing Strategy for Multicomputer Systems - Choi, Esfahanian - 1991 (Show Context) Citation Context ...ness of the decision version of the Steiner tree problem for the n-cube. Later on, a complex transformation and proof was used to establish that the sp-multicast problem for the n-cube is NP-Complete =-=[2, 3]-=-. In this paper we present simple transformations and proofs that establish the NP-Completeness of these two problems. An n-cube (hypercube) consists of 2n vertices or processors. Every vertex in the ...
4	Optimal Routing - Ganesan, Manku - 2004 (Show Context) Citation Context ...em. There is a trivial algorithm to implement optimum unicasting in the n-cube. Optimal polynomial time algorithms for unicasting have been developed for both the Chord and the binomial graph network =-=[4, 5]-=-; however, there has not been a lot of work on multicast in these topologies. It was conjectured 1Traditionally Steiner tree problems are defined for weighted graphs with the objective being to minimi...
3	Optimal routing in binomial graph networks - Angskun, Bosilca, et al. - 2007 (Show Context) Citation Context ...em. There is a trivial algorithm to implement optimum unicasting in the n-cube. Optimal polynomial time algorithms for unicasting have been developed for both the Chord and the binomial graph network =-=[4, 5]-=-; however, there has not been a lot of work on multicast in these topologies. It was conjectured 1Traditionally Steiner tree problems are defined for weighted graphs with the objective being to minimi...