Exponential Time Approximation Scheme For Tsp
ALGORITHMIC ASPECTS IN INFORMATION AND MANAGEMENT, AAIM 2019(2019)
摘要
In this paper, we develop an exponential time approximation scheme for the traveling salesman problem (TSP) on undirected graphs. If the weight of each edge is a nonnegative real number, then there is an algorithm to give an (1 + epsilon) approximation for the TSP problem in O(1/epsilon center dot 1.66(n)) and a polynomial space. It is in contrast to Golovnen's approximation scheme for TSP on directed graphs with O(1/epsilon center dot 2(n)) time. We also show that there is no 2(o(n)) time constant factor approximation for the TSP problem under Exponential Time Hypothesis in complexity theory.
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