# Efficient parallel algorithms for testing connectivity and finding disjoint s-t paths in graphs

Title | Efficient parallel algorithms for testing connectivity and finding disjoint s-t paths in graphs |

Publication Type | Conference Papers |

Year of Publication | 1989 |

Authors | Khuller S, Schieber B |

Conference Name | Foundations of Computer Science, 1989., 30th Annual Symposium on |

Date Published | 1989/11/01/oct |

Keywords | algorithm;parallel, algorithms;random-access, algorithms;testing, complexity;graph, connectivity;computational, connectivity;optimal, CRCW, disjoint, paths;graphs;k-edge, paths;k-vertex, PRAM;disjoint, s-t, speedup, storage;, theory;parallel |

Abstract | An efficient parallel algorithm for testing whether a graph G is K-vertex connected, for any fixed k, is presented. The algorithm runs in O(log n) time and uses nC(n,m) processors on a concurrent-read, concurrent-write parallel random-access machine (CRCW PRAM), where n and m are the number of vertices and edges of G and C(n,m) is the number of processors required to compute the connected components of G in logarithmic time. An optimal speedup algorithm for computing connected components would induce an optimal speedup algorithm for testing k -vertex connectivity, for any k gt;4. To develop the algorithm, an efficient parallel algorithm is designed for the following disjoint s-t paths problem: Given a graph G and two specified vertices s and t, find k-vertex disjoint paths between s and t, if they exist. If no such paths exist, find a set of at most k-1 vertices whose removal disconnects s and t. The parallel algorithm for this problem runs in O(log n) time using C(n,m) processors. It is shown how to modify the algorithm to find k-edge disjoint paths, if they exist. This yields an efficient parallel algorithm for testing whether a graph G is k-edge connected, for any fixed k. The algorithm runs in O(log n) time and uses nC (n,n) processors on a CRCW PRAM. Again, an optimal speedup algorithm for computing connected components would induce an optimal speedup algorithm for testing k-edge connectivity |

DOI | 10.1109/SFCS.1989.63492 |