Approximation result toward nearest neighbor heuristic
In this paper, we revisit the famous heuristic called nearest neighbor (N N) for the traveling salesman problem under maximization and minimization goal. We deal with variants where the edge costs belong to interval Ša;taĆ for a>0 and t>1, which certainly corresponds to practical cases...
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University of Belgrade
2002-01-01
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| Series: | Yugoslav Journal of Operations Research |
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| Online Access: | http://www.doiserbia.nb.rs/img/doi/0354-0243/2002/0354-02430201011M.pdf |
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doaj-afc5e86ee63d4f84b66ce096a24938692020-11-24T22:16:39ZengUniversity of BelgradeYugoslav Journal of Operations Research0354-02431820-743X2002-01-01121111610.2298/YJOR0201011MApproximation result toward nearest neighbor heuristicMonnot Jér"meIn this paper, we revisit the famous heuristic called nearest neighbor (N N) for the traveling salesman problem under maximization and minimization goal. We deal with variants where the edge costs belong to interval Ša;taĆ for a>0 and t>1, which certainly corresponds to practical cases of these problems. We prove that NN is a (t+1)/2t-approximation for maxTSPŠa;taĆ and a 2/(t+1)-approximation for minTSPŠa;taĆ under the standard performance ratio. Moreover, we show that these ratios are tight for some instances. http://www.doiserbia.nb.rs/img/doi/0354-0243/2002/0354-02430201011M.pdfApproximate algorithmsperformance ratioanalysis of algorithmstraveling salesman problem. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Monnot Jér"me |
| spellingShingle |
Monnot Jér"me Approximation result toward nearest neighbor heuristic Yugoslav Journal of Operations Research Approximate algorithms performance ratio analysis of algorithms traveling salesman problem. |
| author_facet |
Monnot Jér"me |
| author_sort |
Monnot Jér"me |
| title |
Approximation result toward nearest neighbor heuristic |
| title_short |
Approximation result toward nearest neighbor heuristic |
| title_full |
Approximation result toward nearest neighbor heuristic |
| title_fullStr |
Approximation result toward nearest neighbor heuristic |
| title_full_unstemmed |
Approximation result toward nearest neighbor heuristic |
| title_sort |
approximation result toward nearest neighbor heuristic |
| publisher |
University of Belgrade |
| series |
Yugoslav Journal of Operations Research |
| issn |
0354-0243 1820-743X |
| publishDate |
2002-01-01 |
| description |
In this paper, we revisit the famous heuristic called nearest neighbor (N N) for the traveling salesman problem under maximization and minimization goal. We deal with variants where the edge costs belong to interval Ša;taĆ for a>0 and t>1, which certainly corresponds to practical cases of these problems. We prove that NN is a (t+1)/2t-approximation for maxTSPŠa;taĆ and a 2/(t+1)-approximation for minTSPŠa;taĆ under the standard performance ratio. Moreover, we show that these ratios are tight for some instances. |
| topic |
Approximate algorithms performance ratio analysis of algorithms traveling salesman problem. |
| url |
http://www.doiserbia.nb.rs/img/doi/0354-0243/2002/0354-02430201011M.pdf |
| work_keys_str_mv |
AT monnotjerme approximationresulttowardnearestneighborheuristic |
| _version_ |
1725788526694367232 |