On Computing Maximal Independent Sets of Hypergraphs in Parallel [article]

Ioana O. Bercea, Navin Goyal, David G. Harris, Aravind Srinivasan
2014 arXiv   pre-print
Whether or not the problem of finding maximal independent sets (MIS) in hypergraphs is in (R)NC is one of the fundamental problems in the theory of parallel computing. Unlike the well-understood case of MIS in graphs, for the hypergraph problem, our knowledge is quite limited despite considerable work. It is known that the problem is in RNC when the edges of the hypergraph have constant size. For general hypergraphs with n vertices and m edges, the fastest previously known algorithm works in
more » ... e O(√(n)) with poly(m,n) processors. In this paper we give an EREW PRAM algorithm that works in time n^o(1) with poly(m,n) processors on general hypergraphs satisfying m ≤ n^^(2)n/8(^(3)n)^2, where ^(2)n = n and ^(3)n = n. Our algorithm is based on a sampling idea that reduces the dimension of the hypergraph and employs the algorithm for constant dimension hypergraphs as a subroutine.
arXiv:1405.1133v2 fatcat:u7agcq4xurextoltyc3ld6bvae