Chapter

Concurrent Computations

pp 117-138

Fast Parallel Algorithms for Reducible Flow Graphs

  • Vijaya RamachandranAffiliated withUniversity of Illinois

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Abstract

We give parallel NC algorithms for recognizing reducible flow graphs (rfg’s), and for finding dominators, minimum feedback vertex sets, and a depth first search numbering in an rfg. We show that finding a minimum feedback vertex set in vertex-weighted rfg’s or finding a minimum feedback arc set in arc-weighted rfg’s is P-complete. We present RNC algorithms for finding a minimum feedback arc set in an unweighted rfg, and for finding a minimum weight feedback set when arc or vertex weights are in unary; and we show that these problems are in NC if and only if the maximum matching problem is in NC.