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Lower Bounds for Insertion Methods for TSP

Published online by Cambridge University Press:  12 September 2008

Yossi Azar
Yossi Azar
Affiliation:
Department of Computer Science, Tel-Aviv University, Israel
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Abstract

We show that the random insertion method for the traveling salesman problem (TSP) may produce a tour Ω(log log n/log log log n) times longer than the optimal tour. The lower bound holds even in the Euclidean Plane. This is in contrast to the fact that the random insertion method performs extremely well in practice. In passing, we show that other insertion methods may produce tours Ω(log n/log log n) times longer than the optimal one. No non-constant lower bounds were previously known.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 3 , Issue 3 , September 1994 , pp. 285 - 292
Copyright
Copyright © Cambridge University Press 1994

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