The approximability of problems complete for P
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We examine here the existence of approximations in NC of P-complete problems. We show that many P-complete problems (such as UNIT, PATH, circuit value etc.) cannot have an approximating solution in NC for any value of the absolute performance ratio R of the approximation, unless P=NC. On the other hand, we exhibit of a purely combinatorial problem (the High Connectivity subgraph problem) whose behaviour with respect to fast parallel approximations is of a threshold type. This dichotomy in the behaviour of approximations of P-complete problems is for the first time revealed and we show how the tools of log-space reductions can be used to make inferences about the best possible performance of approximations of problems that are hard to parallelize.
KeywordsNode Pair Optimization Version Vertex Connectivity Gate Input Linear Reduction
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