travelling_salesman_problem
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travelling_salesman_problem [2024/04/21 17:46] 47.128.60.32 old revision restored (2024/04/18 13:37) |
travelling_salesman_problem [2024/04/21 18:44] (current) 47.128.47.250 old revision restored (2024/04/17 14:28) |
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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 | + | 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. |
| 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. | ||
travelling_salesman_problem.txt · Last modified: 2024/04/21 18:44 by 47.128.47.250
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