On the shortest length queries for permutation graphs

Abstract

The all-pairs shortest path problem is a very important problem for both theoretical researches and practical applications. Given an undirected, unweighted, connected graph of n vertices, computing the lengths of the shortest paths between all pairs of vertices takes Ω(n²)time and space, since there are θ(n²)pairs of vertices. In this paper, we present efficient algorithms to solve the query version for the problem of computing the lengths of all-pairs shortest paths for permutation graphs. Given a permutation graph G,our algorithms preprocess G in O(logn)time using O(n/logn)processors under the EREW PRAM model such that the shortest length query between any two vertices can be answered in O(1) time using one processor.