Geodesic
Approximation Results Toward Nearest Neighbor Heuristic
Yugoslav journal of operations research, Tome 12 (2002) no. 1, p. 11 .

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In this paper, we revisit the famous heuristic called nearest neighbor ($NN$ ) for the traveling salesman problem under maximization and minimization goal. We deal with variants where the edge costs belong to interval $[a;ta]$ 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 max $TSP[a;ta]$ and $2/(t+1)$ -approximation for min $TSP[a;ta]$ under the standard performance ratio. Moreover, we show that these ratios are tight for some instances.
Classification : 90C59 90C27
Keywords: Approximate algorithms, performance ratio, analysis of algorithms, traveling salesman problem. 
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     author = {J\'er\^ome Monnot},
     title = {Approximation {Results} {Toward} {Nearest} {Neighbor} {Heuristic}},
     journal = {Yugoslav journal of operations research},
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     publisher = {mathdoc},
     volume = {12},
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     year = {2002},
     zbl = {1045.90089},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/YJOR_2002_12_1_a1/}
}
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Jérôme Monnot. Approximation Results Toward Nearest Neighbor Heuristic. Yugoslav journal of operations research, Tome 12 (2002) no. 1, p. 11 . http://geodesic.mathdoc.fr/item/YJOR_2002_12_1_a1/