Elsevier

Journal of Algorithms

Volume 10, Issue 2, June 1989, Pages 249-270
Journal of Algorithms

The parallel complexity of TSP heuristics

https://doi.org/10.1016/0196-6774(89)90015-1Get rights and content

Abstract

We consider eight heuristics for constructing approximate solutions to the traveling salesman problem and analyze their complexity in a model of parallel computation. The problems of finding a tour by the nearest neighbor, nearest merger, nearest insertion, cheapest insertion, and farthest insertion heuristics are shown to be P-complete. Hence, it is unlikely that such tours can be obtained in polylogarithmic work space on a sequential computer or in polylogarithmic time on a computer with unbounded parallelism. The double minimum spanning tree and nearest addition heuristics can be implemented to run in polylogarithmic time on a polynomial number of processors. For the Christofides heuristic, we give a randomized polylogarithmic approximation scheme requiring a polynomial number of processors.

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