An efficient deterministic parallel algorithm for two processors precedence constraint scheduling

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Hermann Jung, Maria J. Serna, Paul G. Spirakis

Published: 2003, Last Modified: 09 May 2025Theor. Comput. Sci. 2003EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: We present here a new deterministic parallel algorithm for the two-processor scheduling problem. The algorithm uses only O(n3)<math><mtext>O</mtext><mtext>(n</mtext><msup><mi></mi><mn>3</mn></msup><mtext>)</mtext></math> processors and takes O(log2n)<math><mtext>O</mtext><mtext>(</mtext><mtext>log</mtext><msup><mi></mi><mn>2</mn></msup><mtext>n)</mtext></math> time on a CREW PRAM. In order to prove the above bounds we show how to compute in NC the lexicographically first matching for a special kind of convex bipartite graphs.