An Approximate Algorithm for TSP with Four Vertices and Three Lines Inequality

Authors

Yon Wang, School of Renewable Energy, North China Electric Power University, 102206 Beijing, ChinaFollow

Abstract

If the distances of TSP satisfy the triangle inequality, the minimum-cost-spanning tree (MST) heuristics produces a tour whose length is guaranteed to be less than 2 times the optimum tour length and Christofides’ heuristics generates the 3/2 times the optimum tour length. Otherwise, the quality of the approximation is hard to evaluate. Here a four vertices and three lines inequality is used to construct an approximation of the optimum tour instead of the triangle inequality. The performance ratio of the heuristics may not be a constant for all kinds of TSP. But it is determined for a concrete TSP.

Recommended Citation

Wang, Yon (2014) "An Approximate Algorithm for TSP with Four Vertices and Three Lines Inequality," Information Sciences Letters: Vol. 3 : Iss. 2 , PP -.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol3/iss2/1