Summary: Smoothed Analysis of Partitioning Algorithms
for Euclidean Functionals
, Bodo Manthey2
, and B. V. Raghavendra Rao1
Saarland University, Department of Computer Science
University of Twente, Department of Applied Mathematics
Abstract. Euclidean optimization problems such as TSP and mini-
mum-length matching admit fast partitioning algorithms that compute
near-optimal solutions on typical instances.
In order to explain this performance, 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 Frie-
ze's partitioning algorithm for Euclidean matching, Karp's partitioning