The Community for Technology Leaders
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
85 ms
(Ver 3.3 (11022016))