- The best essay writing company you will ever find online
- +1 (510) 327 2058
- support@bestessayswriters.com

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

We use cookies to ensure that we give you the best experience on our website. If you continue to use this site we will assume that you are happy with it.Ok