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Preprints 1999

Implementing Weighted b-Matching Algorithms: Insights from a Computational Study
Citation key Report-631-1999
Author Müller-Hannemann, Matthias and Schwartz, Alexander
Year 1999
Number 631
Note extended abstract in Proceedings of the Workshop on Algorithm Engineering and Experimentation (ALENEX99), Baltimore, Maryland, USA, Lecture Notes in Computer Science, vol. 1619, pp. 18-36, Springer-Verlag-Verlag
Institution Technische Universität Berlin, Institut für Mathematik
Abstract We present an experimental study of an implementation of weighted perfect b-matching based on Pulleyblank's algorithm (1973). Although this problem is well-understood in theory and efficient algorithms are known, only little experience with implementations is available. In this paper several algorithmic variants are compared on synthetic and application problem data of very sparse graphs. This study was motivated by the practical need for an efficient b-matching solver for an industrial application, namely as a subroutine in our approach to a mesh refinement problem in computer-aided design (CAD). Linear regression and operation counting is used to analyze code variants. The experiments indicate that a fractional jump-start should be used, a priority queue within the dual update helps, scaling of b-values is not necessary, whereas a delayed blossom shrinking heuristic significantly improves running times only for graphs with average degree two. The fastest variant of our implementation appears to be highly superior to a code by Miller and Pekny (1995).
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