A polynomial algorithm for b-matchings: an alternative approach
Information Processing Letters
A faster strongly polynomial minimum cost flow algorithm
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Handbook of combinatorics (vol. 1)
Mesh refinement via bidirected flows: modeling, complexity, and computational results
Journal of the ACM (JACM)
Complexity and Modeling Aspects of Mesh Refinement into Quadrilaterals
ISAAC '97 Proceedings of the 8th International Symposium on Algorithms and Computation
Implementing Weighted b-Matching Algorithms: Insights from a Computational Study
ALENEX '99 Selected papers from the International Workshop on Algorithm Engineering and Experimentation
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Matching algorithms.
Implementing Weighted b-Matching Algorithms: Insights from a Computational Study
ALENEX '99 Selected papers from the International Workshop on Algorithm Engineering and Experimentation
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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 Miller & Pekny (1995).