travelling_salesman_problem
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travelling_salesman_problem [2024/05/03 15:45] 47.128.97.167 old revision restored (2024/04/29 15:37) |
travelling_salesman_problem [2024/05/18 13:16] (current) 170.106.99.139 old revision restored (2024/05/12 14:17) |
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| === Complexity of approximation === | === Complexity of approximation === | ||
| - | In the general case, finding a shortest travelling salesman tour is NPO-complete. If the distance measure is a metric and symmetric, the problem becomes APX-complete and Christofides’s algorithm approximates it within 1.5. | + | In the general case, finding a shortest travelling salesman tour is NPO-complete. If the distance measure is a metric and symmetric, the problem becomes |
| If the distances are restricted to 1 and 2 (but still are a metric) the approximation ratio becomes 8/7. In the asymmetric, metric case, only logarithmic performance guarantees are known, the best current algorithm achieves performance ratio $0.814 log(n)$; it is an open question if a constant factor approximation exists. | If the distances are restricted to 1 and 2 (but still are a metric) the approximation ratio becomes 8/7. In the asymmetric, metric case, only logarithmic performance guarantees are known, the best current algorithm achieves performance ratio $0.814 log(n)$; it is an open question if a constant factor approximation exists. | ||
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