Abstract
The shortest-paths problem is a fundamental problem in graph theory and finds diverse applications in various fields. This is why shortest path algorithms have been designed more thoroughly than any other algorithm in graph theory. A large number of optimization problems are mathematically equivalent to the problem of finding shortest paths in a graph. The shortest-path between a pair of vertices is defined as the path with shortest length between the pair of vertices. The shortest path from one vertex to another often gives the best way to route a message between the vertices. This paper presents anO(n 2) time sequential algorithm and anO(n 2/p+logn) time parallel algorithm on EREW PRAM model for solving all pairs shortest paths problem on circular-arc graphs, wherep andn represent respectively the number of processors and the number of vertices of the circular-arc graph.
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Anita Saha received her M. Sc from Vidyasagar University, India in 2000. She has started her Ph. D. work at Vidyasagar University on 2000. Her research interests include computational graph theory, parallel algorithms, data structure.
Madhumangal Pal received his M. Sc from Vidyasagar University, India and Ph. D from Indian Institute of Technology, Kharagpur, India in 1990 and 1996 respectively. He is engaged in research since 1991. In 1996, he received Computer Division Award from Institution of Engineers (India), for best research work. During 1997 to 1999 he was a faculty member of Midnapore College and since 1999 he has been at the Vidyasagar University, India. His research interest include computational graph theory, parallel algorithms, data structure, combinatorial algorithms, genetic algorithms, fuzzy sets and intuitionistic fuzzy sets.
Tapan K. Pal received his M. Sc in 1971 and Ph. D in 1982 from Indian Institute of Technology, Kharagpur, India. During 1971 to 1987 he was a faculty member of Kharagpur College and since 1987 he has been at the Vidyasagar University, India. His research interest includes Operations Research, Graph Theory and Functional Analysis.
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Saha, A., Pal, M. & Pal, T.K. An optimal parallel algorithm for solving all-pairs shortest paths problem on circular-arc graphs. JAMC 17, 1–23 (2005). https://doi.org/10.1007/BF02936037
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DOI: https://doi.org/10.1007/BF02936037