Abstract
For the traveling salesman problem in which the distances satisfy the triangle inequality, Christofides' heuristic produces a tour whose length is guaranteed to be less than 3/2 times the optimum tour length. We investigate the performance of appropriate modifications of this heuristic for the problem of finding a shortest Hamiltonian path. There are three variants of this problem, depending on the number of prespecified endpoints: zero, one, or two. It is not hard to see that, for the first two problems, the worst-case performance ratio of a Christofides-like heuristic is still 3/2. For the third case, we show that the ratio is 5/3 and that this bound is tight.
Original language | English |
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Pages (from-to) | 291-295 |
Number of pages | 5 |
Journal | Operations Research Letters |
Volume | 10 |
Issue number | 5 |
DOIs | |
Publication status | Published - 1991 |