travelling_salesman_problem
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travelling_salesman_problem [2017/03/27 05:59] ntcnet [Computational complexity] |
travelling_salesman_problem [2024/04/25 14:28] (current) 47.128.45.100 old revision restored (2024/04/21 17:10) |
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| ===== Computing a solution ===== | ===== Computing a solution ===== | ||
| - | <note tip> | + | ==== Computational complexity ==== |
| The problem has been shown to be NP-hard (more precisely, it is complete for the complexity class FPNP; see function problem), and the decision problem version (" | The problem has been shown to be NP-hard (more precisely, it is complete for the complexity class FPNP; see function problem), and the decision problem version (" | ||
| === 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 | + | 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.1490608751.txt.gz · Last modified: 2017/03/27 05:59 by ntcnet
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