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CS Algorithm Homework question




Consider the following heuristic for building an approximate traveling-salesman tour, assuming;that the edge weights satisfy the triangle inequality. Begin with a trivial cycle consisting of a;singe arbitrarily chosen vertex. At each step, identify the vertex u that is not yet on the cycle;but whose distance to any vertex on the cycle is minimum (that is, if C is the current cycle;for every vertex w 62 C compute the number d(w) = minv2C dist(w, v) and choose the vertex u;for which d(u) is minimum). Suppose that the vertex on the cycle that is nearest to u is vertex;v. Extend the cycle to include u by inserting u just after v. Repeat until all vertices are on the;cycle. Prove that this heuristic returns a tour whose total cost is not more than twice the cost;of an optimal tour.


Paper#72657 | Written in 18-Jul-2015

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