Computing maximum matchings in temporal graphs

Mertzios, G.B.; Molter, H.; Niedermeier, R.; Zamaraev, V.; Zschoche, P.

Abstract

Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph G, a temporal graph is represented by assigning a set of integer time-labels to every edge e of G, indicating the discrete time steps at which e is active. We introduce and study the complexity of a natural temporal extension of the classical graph problem Maximum Matching, taking into account the dynamic nature of temporal graphs. In our problem, Maximum Temporal Matching, we are looking for the largest possible number of time-labeled edges (simply time-edges) (e, t) such that no vertex is matched more than once within any time window of ∆ consecutive time slots, where ∆ ∈ N is given. We prove strong computational hardness results for Maximum Temporal Matching, even for elementary cases, as well as fixed-parameter algorithms with respect to natural parameters and polynomial-time approximation algorithms.

Citation

Mertzios, G., Molter, H., Niedermeier, R., Zamaraev, V., & Zschoche, P. (in press). Computing maximum matchings in temporal graphs. Journal of Computer and System Sciences, https://doi.org/10.1016/j.jcss.2023.04.005

• Journal Article Type: Article
• Acceptance Date: Apr 21, 2023
• Online Publication Date: May 4, 2023
• Deposit Date: May 10, 2023
• Publicly Available Date: May 5, 2024
• Journal: Journal of Computer and System Sciences
• Print ISSN: 0022-0000
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1016/j.jcss.2023.04.005