Smoothed analysis of partitioning algorithms for Euclidean functionals

Authors:
Markus Bläser;Bodo Manthey;B. V. Raghavendra Rao
Affiliations:
Saarland University, Department of Computer Science;University of Twente, Department of Applied Mathematics;Saarland University, Department of Computer Science
Venue:
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Year:
2011

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Abstract

Euclidean optimization problems such as TSP and minimum-length matching admit fast partitioning algorithms that compute near-optimal solutions on typical instances. We develop a general framework for the application of smoothed analysis to partitioning algorithms for Euclidean optimization problems. Our framework can be used to analyze both the running-time and the approximation ratio of such algorithms. We apply our framework to obtain smoothed analyses of Dyer and Frieze's partitioning algorithm for Euclidean matching, Karp's partitioning scheme for the TSP, a heuristic for Steiner trees, and a heuristic for degree-bounded minimum-length spanning trees.