A probabilistic analysis of christofides' algorithm

Authors:
Markus Bläser;Konstatinos Panagiotou;B. V. Raghavendra Rao
Affiliations:
Department of Computer Science, Saarland University, Germany;Department of Mathematics, University of Munich, Germany;Department of Computer Science, Saarland University, Germany
Venue:
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Year:
2012

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Abstract

Christofides' algorithm is a well known approximation algorithm for the metric travelling salesman problem. As a first step towards obtaining an average case analysis of Christofides' algorithm, we provide a probabilistic analysis for the stochastic version of the algorithm for the Euclidean traveling salesman problem, where the input consists of n randomly chosen points in [0,1]d. Our main result provides bounds for the length of the computed tour that hold almost surely. We also provide an experimental evaluation of Christofides's algorithm.