Efficient Parallel Algorithms for Doubly Convex-Bipartite Graphs

Abstract Suppose that G = (S, T, E) is a bipartite graph. An ordering of S(T) has the adjacency property if for each vertex in T(S), its adjacent vertices in S(T) are consecutive in the ordering. If there exist orderings of S and T which have the adjacency property, G is called a doubly convex-bipartite graph. In this paper, a parallel algorithm is proposed to recognize a doubly convex-bipartite graph. The algorithm runs in O(log n) time using O( n 3 log n ) processors on the CRCW PRAM, or O(log2 n) time using O( n 3 log 2 n) processors on the CREW PRAM.

[1]  Sartaj Sahni,et al.  A parallel matching algorithm for convex bipartite graphs and applications to scheduling , 1984, J. Parallel Distributed Comput..

[2]  Gen-Huey Chen,et al.  An Efficient Parallel Recognition Algorithm For Bipartite-Permutation Graphs , 1996, IEEE Trans. Parallel Distributed Syst..

[3]  M. Golumbic.  Algorithmic graph theory and perfect graphs , 1980 .

[4]  Lin Chen,et al.  Parallel Recognition of the Consecutive Ones Property with Applications , 1991, J. Algorithms.

[5]  Wojciech Rytter,et al.  Efficient parallel algorithms , 1988 .

[6]  Uzi Vishkin,et al.  An O(log n) Parallel Connectivity Algorithm , 1982, J. Algorithms.

[7]  Francis Y. L. Chin,et al.  Efficient parallel algorithms for some graph problems , 1982, CACM.

[8]  Richard Cole,et al.  Parallel merge sort , 1988, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[9]  F. Glover.  Maximum matching in a convex bipartite graph , 1967 .

[10]  Jeremy P. Spinrad,et al.  Bipartite permutation graphs , 1987, Discret. Appl. Math..

[11]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[12]  Philip N. Klein,et al.  An efficient parallel algorithm for planarity , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[13]  Leizhen Cai,et al.  NP-completeness of edge-colouring some restricted graphs , 1991, Discret. Appl. Math..

[14]  Uzi Vishkin,et al.  On Efficient Parallel Strong Orientation , 1985, Inf. Process. Lett..