Approximation algorithms for maximum matchings in undirected graphs

Fanny Dufossé (1) , Kamer Kaya (2) , Ioannis Panagiotas (3) , Bora Uçar (4)

1 DOLPHIN - Parallel Cooperative Multi-criteria Optimization
2 Sabanci University - Faculty of Engineering and Natural Sciences
3 ENS de Lyon - École normale supérieure de Lyon
4 ROMA - Optimisation des ressources : modèles, algorithmes et ordonnancement

We propose heuristics for approximating the maximum cardinality matching on undirected graphs. Our heuristics are based on the theoretical body of a certain type of random graphs, and are made practical for real-life ones. The idea is based on judiciously selecting a subgraph of a given graph and obtaining a maximum cardinality matching on this subgraph. We show that the heuristics have an approximation guarantee of around 0.866 − log(n)/n for a graph with n vertices. Experiments for verifying the theoretical results in practice are provided.

Domaines: Informatique [cs]; Algorithme et structure de données [cs.DS]

Fanny Dufossé, Kamer Kaya, Ioannis Panagiotas, Bora Uçar. Approximation algorithms for maximum matchings in undirected graphs. SIAM Workshop on Combinatorial Scientific Computing 2018 (CSC18), Jun 2018, Bergen, Norway. ⟨hal-01740403v1⟩