Implementing weighted b-matching algorithms: towards a flexible software design

We present a case study on the design of an implementation of a fundamental combinatorial optimization problem: weighted <i>b</i>-matching. Although this problem is well-understood in theory and efficient algorithms are known, only little experience with implementations is available. This study was motivated by the practical need for an efficient <i>b</i>-matching solver as a subroutine in our approach to a mesh refinement problem in computer-aided design (CAD).The intent of this paper is to demonstrate the importance of flexibility and adaptability in the design of complex algorithms, but also to discuss how such goals can be achieved for matching algorithms by the use of design patterns. Starting from the basis of the famous blossom algorithm we explain how to exploit in different ways the flexibility of our software design which allows an incremental improvement of efficiency by exchanging subalgorithms and data structures.In a comparison with a code by Miller and Pekny we also demonstrate that our implementation is even without fine-tuning very competitive. Our code is significantly faster, with improvement factors ranging between 15 and 466 on TSPLIB instances.

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