Parallel Algorithms / Architecture Synthesis, AIZU International Symposium on (1995)

Aizu-Wakamatsu, Fukushima, Japan

Mar. 15, 1995 to Mar. 17, 1995

ISBN: 0-8186-7038-X

pp: 169

Zhi-Zhong Chen , Dept. of Math. Sci., Tokyo Denki Univ., Saitama, Japan

Xin He , Dept. of Math. Sci., Tokyo Denki Univ., Saitama, Japan

ABSTRACT

Given a graph G=(V, E), the classical spanning forest problem of G can be viewed as the problem of finding a maximal subset F of E inducing an acyclic subgraph. Although it is well known that this problem has efficient NC algorithms, its vertex counterpart, i.e., the problem of finding a maximal subset U of V inducing an acyclic subgraph, has not been shown to be in NC (or even in RNC) and is not believed to be parallelizable in general. We present NC algorithms for solving the latter problem for three special cases. The first algorithm solves the problem for planar graphs in O(log/sup 3/ n) time using O(n) processors on an EREW PRAM. The second algorithm solves the problem for K/sub 3,3/-free graphs in O(log/sup 4/ n) time using O(n) processors on an EREW PRAM. The third algorithm solves the problem for graphs without long induced paths in poly-logarithmic time using O(n/sup 2376/) processors on an EREW PRAM.

INDEX TERMS

parallel algorithms; graph theory; computational complexity; set theory; maximal acyclic sets; parallel algorithms; graph; classical spanning forest problem; maximal subset; acyclic subgraph; planar graphs; processors; EREW PRAM; poly-logarithmic time

CITATION

Zhi-Zhong Chen,
Xin He,
"Parallel algorithms for maximal acyclic sets",

*Parallel Algorithms / Architecture Synthesis, AIZU International Symposium on*, vol. 00, no. , pp. 169, 1995, doi:10.1109/AISPAS.1995.401341