An optimal parallel algorithm for solving all-pairs shortest paths problem on circular-arc graphs

Abstract

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 an O(n 2 ) time sequential algorithm and an O(n 2 /p + log n) time parallel algorithm on EREW PRAM model for solving all pairs shortest paths problem on circular-arc graphs, where p and n represent respectively the number of processors and the number of vertices of the circular-arc graph.

An Optimal Algorithm to Find Next-to-Shortest Path between Two Vertices of Cactus Graphs

“…Maity and Pal [20] have designed an optimal algorithm to solve APSP problem on cactus graphs. In [31], Saha et al have designed an optimal algorithm to find APSP on circular-arc graphs. In [8], Eppstein has designed an algorithm for finding the -shortest paths in a digraph with vertices and edges in time.…”

A survey of the all-pairs shortest paths problem and its variants in graphs

“…A few open problems related to the distances are also suggested. Later, Mondal et al [59] and Saha et al [69] obtained optimal algorithms for solving APSP on the class of trapezoid graphs and circular arc graphs respectively. For the definition of various families of graphs [8,33] may be consulted.…”

L(2,1)-labeling of interval graphs

“…Thus finding good upper bounds of these graphs is a good result. Circular-arc graph is a very important subclass of intersection graphs and has been widely studied in the past [34,35,36,50]. Many works have been done on other intersections graphs, see [2,3,15,22,23,[31][32][33][38][39][40][41][42][43][44]49,[51][52][53].…”