Abstract
P-complete problems are those that can be solved on an available computer with a single processor, taking (at most) polynomial time. Problems with polynomial complexity are the first potential candidates among “hard” problems that we should solve efficiently on future parallel computers. With parallel computation, we can solve such problems in subpolynomial time on a polynomial number of processors running concurrently on the problem solution— but space limits the number of processors. Additionally, communication time increases rapidly with an increase in the number of processors. According to the authors of Limits to Parallel Computation: P-Completeness Theory, a highly parallel algorithm is not feasible today if the number of processors required for a problem of size N is greater than N log N. This book helps prepare readers for the available processing power of future computers and warns
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