Strict Sequential P-completeness

In this paper we present a new notion of what it means for a problem in P to be inherently sequential. Informally, a problem L is strictly sequential P-complete if when the best known sequential algorithm for L has polynomial speedup by parallelization, this implies that all problems in P have a polynomial speedup in the parallel setting. The motivation for defining this class of problems is to try and capture the problems in P that are truly inherently sequential. Our work extends the results of Condon who exhibited problems such that if a polynomial speedup of their best known parallel algorithms could be achieved, then all problems in P would have polynomial speedup. We demonstrate one such natural problem, namely the Multiplex-select Circuit Problem (MCP). MCP has one of the highest degrees of sequentiality of any problem yet defined. On the way to proving MCP is strictly sequential Pcomplete, we define an interesting model, the register stack machine, that appears to be of inde...

• Type: Conference
• Year: 1997
• Where: STACS
• Authors: Klaus Reinhardt
• Keywords: Polynomial Speedup, Problems, Sequential, STACS 1997, Theoretical Computer Science