Preemptive online algorithms for the maximum matching problem maintain a valid matching M while edges of the underlying graph are presented one after the other. When presented with an edge e, the algorithm should decide whether to augment the matching M by adding e (in which case e may be removed later on) or to keep M in its current form without adding e (in which case e is lost for good). The objective is to eventually hold a matching M with maximum weight. The main contribution of this paper is to establish new lower and upper bounds on the competitive ratio achievable by randomized preemptive online algorithms: • We provide a lower bound of 1+ln2≈1.693 on the competitive ratio of any randomized algorithm for the maximum cardinality matching problem.• We devise a randomized algorithm that achieves an expected competitive ratio of 5.356 for maximum weight matching.
Bibliographical notePublisher Copyright:
© 2017 Elsevier Inc.
- Competitive analysis
- Lower bounds
- Online matching
ASJC Scopus subject areas
- Theoretical Computer Science
- Information Systems
- Computer Science Applications
- Computational Theory and Mathematics