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Weighted Graphs (weighted + graph)

Distribution by Scientific Domains
Information Science and Computing57%

Selected Abstracts

A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs,

RANDOM STRUCTURES AND ALGORITHMS, Issue 4 2007
Surender Baswana
Abstract Let G = (V,E) be an undirected weighted graph on |V | = n vertices and |E| = m edges. A t -spanner of the graph G, for any t , 1, is a subgraph (V,ES), ES , E, such that the distance between any pair of vertices in the subgraph is at most t times the distance between them in the graph G. Computing a t -spanner of minimum size (number of edges) has been a widely studied and well-motivated problem in computer science. In this paper we present the first linear time randomized algorithm that computes a t -spanner of a given weighted graph. Moreover, the size of the t -spanner computed essentially matches the worst case lower bound implied by a 43-year old girth lower bound conjecture made independently by Erd,s, Bollobás, and Bondy & Simonovits. Our algorithm uses a novel clustering approach that avoids any distance computation altogether. This feature is somewhat surprising since all the previously existing algorithms employ computation of some sort of local or global distance information, which involves growing either breadth first search trees up to ,(t)-levels or full shortest path trees on a large fraction of vertices. The truly local approach of our algorithm also leads to equally simple and efficient algorithms for computing spanners in other important computational environments like distributed, parallel, and external memory. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007 [source]

Shortest paths in fuzzy weighted graphs

INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 11 2004
Chris Cornelis
The task of finding shortest paths in weighted graphs is one of the archetypical problems encountered in the domain of combinatorial optimization and has been studied intensively over the past five decades. More recently, fuzzy weighted graphs, along with generalizations of algorithms for finding optimal paths within them, have emerged as an adequate modeling tool for prohibitively complex and/or inherently imprecise systems. We review and formalize these algorithms, paying special attention to the ranking methods used for path comparison. We show which criteria must be met for algorithm correctness and present an efficient method, based on defuzzification of fuzzy weights, for finding optimal paths. © 2004 Wiley Periodicals, Inc. Int J Int Syst 19: 1051,1068, 2004. [source]

A measure for the cohesion of weighted networks

JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE AND TECHNOLOGY, Issue 3 2003
Leo Egghe
A generalization of both the Botafogo-Rivlin-Shneiderman compactness measure and the Wiener index is presented. These new measures for the cohesion of networks can be used in case a dissimilarity value is given between nodes in a network or a graph. It is illustrated how a set of weights between connected nodes can be transformed into a set of dissimilarity measures for all nodes. The new compactness measure for the cohesion of weighted graphs has several desirable properties related to the disjoint union of two networks. Finally, an example is presented of the calculation of the new compactness measures for a co-citation and a bibliographic coupling network. [source]

A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs,

RANDOM STRUCTURES AND ALGORITHMS, Issue 4 2007
Surender Baswana
Abstract Let G = (V,E) be an undirected weighted graph on |V | = n vertices and |E| = m edges. A t -spanner of the graph G, for any t , 1, is a subgraph (V,ES), ES , E, such that the distance between any pair of vertices in the subgraph is at most t times the distance between them in the graph G. Computing a t -spanner of minimum size (number of edges) has been a widely studied and well-motivated problem in computer science. In this paper we present the first linear time randomized algorithm that computes a t -spanner of a given weighted graph. Moreover, the size of the t -spanner computed essentially matches the worst case lower bound implied by a 43-year old girth lower bound conjecture made independently by Erd,s, Bollobás, and Bondy & Simonovits. Our algorithm uses a novel clustering approach that avoids any distance computation altogether. This feature is somewhat surprising since all the previously existing algorithms employ computation of some sort of local or global distance information, which involves growing either breadth first search trees up to ,(t)-levels or full shortest path trees on a large fraction of vertices. The truly local approach of our algorithm also leads to equally simple and efficient algorithms for computing spanners in other important computational environments like distributed, parallel, and external memory. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007 [source]