Parallel connectivity algorithms on permutation graphs

In this paper, we shall present several algorithms for determining the maximum number of vertex connectivity, testing k-vertex connectivity, determining the maximum number of vertex disjoint s-t paths and finding k-vertex disjoint s-t paths problems on a permutation graph, respectively. We first give several O(n/sup 2/) time sequential algorithms for determining the maximum number of vertez connectivity, testing k-vertex connectivity and determining the maximum number of vertex disjoint s-t paths problems, respectively. Then, an O(kn/sup 2/) time algorithm for finding k-vertex disjoint s-t paths problem on a permutation graph is also proposed. Moreover, we also derive the corresponding parallel algorithms for these problems from the proposed sequential algorithms. On the EREW PRAM model, we first propose several O(log n) time optimal speed-tip parallel algorithms for determining the maximum m number of vertez connectivity, testing k-vertex connectivity and determining the maximum number of vertex disjoint s-t paths problems, all with O(n/sup 2/log n) processors, respectively. Then, an O(nlog n) time parallel algorithm for finding k-vertex disjoint s-t paths problem using O(n/sup 2/log n) processors is also developed, where k is a fixed integer.<>