Parallel Complexity and P-Complete Problems.
Satoru Miyano · QIR (Kyushu University Institutional Repository) (Kyushu University) · 1988
The class NC consists of probiem solvable by parallel algorithms running in time $ Oleft((log n)^k/right) $ using polynomial number of processors for some $ k gep 0 $. It is strongly believed that $ P \\eq NC $ . If $ P \\eq NC $ is assumed, the P-completeness of a problem implies that no eficient parallel algorithm exists for the problem. This paper presents very general P-comp!eteness theorems which yield a new series of P-complete problems including the lexicographically first maximal independent set problem (Cook 1983). We also give a rnethod of firding parallelisrn in some kind of sequential algorithms.