Shrinking trees not blossoms: A recursive maximum matching approach

Abstract

We suggest new concepts for engineering maximum matching algorithms on general graphs which can be used as alternatives in augmenting path approaches such as, e.g., Edmonds or Micali and Vazirani. Our newly introduced alternating rooted sets (ARSs) for finding augmenting paths generalize the state-of-the-art alternating trees. In order to realize an ARS approach on multiple growing trees, we suggest the cherry tree data structure that does not only avoid explicit blossom shrinking but also supports a rotation operation. This operation allows for determining maximum sets of augmenting paths with respect to the given ARSs. These sets can be found by solving a maximum matching problem in the metagraph arising by shrinking the ARSs. We experimentally evaluate our new recursive metagraph approach on a wide set of benchmark instances including a comparison to publically available state-of-the-art software.