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The parallel complexity of approximation algorithms for the maximum acyclic subgraph problem

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Abstract

Several classes of sequential algorithms to approximate themaximum acyclic subgraph problem are examined. The equivalentfeedback arc set problem isNP-complete and there are only a few classes of graphs for which it is known to be inP. Thus, approximation algorithms are very important for this problem. Our goal is to determine how effectively the various sequential algorithms parallelize. Of the sequential algorithms we study, natural decision problems based on several of them are provedP-complete. Parallel implementations usingO(log ¦V¦) time and ¦E¦ processors on an EREW PRAM exist for the other algorithms. Interestingly, the parallelizable algorithms appear very similar to some of theinherently sequential algorithms. Thus, for approximating the maximum acyclic subgraph problem small algorithmic changes drastically alter parallel complexity, unlessNC equalsP.

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  1. Department of Computer Science, University of New Hampshire, 03824, Durham, NH, USA

    Raymond Greenlaw

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Greenlaw, R. The parallel complexity of approximation algorithms for the maximum acyclic subgraph problem. Math. Systems Theory 25, 161–175 (1992). https://doi.org/10.1007/BF01374523

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