Implementing Weighted b-Matching Algorithms: Insights from a Computational Study

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 the latter 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 (1995).