A faster parameterized algorithm for temporal matching
A temporal graph is a sequence of graphs (called layers) over the same vertex set—describing a graph topology which is subject to discrete changes over time. A Δ-temporal matching M is a set of time edges (e,t) (an edge e paired up with a point in time t) such that for all distinct time edges (e,t),...
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| Published in | Information processing letters Vol. 174; p. 106181 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
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Elsevier B.V
01.03.2022
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| Online Access | Get full text |
| ISSN | 0020-0190 1872-6119 |
| DOI | 10.1016/j.ipl.2021.106181 |
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| Abstract | A temporal graph is a sequence of graphs (called layers) over the same vertex set—describing a graph topology which is subject to discrete changes over time. A Δ-temporal matching M is a set of time edges (e,t) (an edge e paired up with a point in time t) such that for all distinct time edges (e,t),(e′,t′)∈M we have that e and e′ do not share an endpoint, or the time-labels t and t′ are at least Δ time units apart. Mertzios et al. [STACS '20] provided a 2O(Δν)⋅|G|O(1)-time algorithm to compute the maximum size of a Δ-temporal matching in a temporal graph G, where |G| denotes the size of G, and ν is the Δ-vertex cover number of G. The Δ-vertex cover number is the minimum number ν such that the classical vertex cover number of the union of any Δ consecutive layers of the temporal graph is upper-bounded by ν. We show an improved algorithm to compute a Δ-temporal matching of maximum size with a running time of ΔO(ν)⋅|G| and hence provide an exponential speedup in terms of Δ.
•An exponential speedup for Temporal Matching compared to the algorithm from Mertzios et al. [STACS '20].•Representing Δ-windows in a tree structure. |
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| AbstractList | A temporal graph is a sequence of graphs (called layers) over the same vertex set—describing a graph topology which is subject to discrete changes over time. A Δ-temporal matching M is a set of time edges (e,t) (an edge e paired up with a point in time t) such that for all distinct time edges (e,t),(e′,t′)∈M we have that e and e′ do not share an endpoint, or the time-labels t and t′ are at least Δ time units apart. Mertzios et al. [STACS '20] provided a 2O(Δν)⋅|G|O(1)-time algorithm to compute the maximum size of a Δ-temporal matching in a temporal graph G, where |G| denotes the size of G, and ν is the Δ-vertex cover number of G. The Δ-vertex cover number is the minimum number ν such that the classical vertex cover number of the union of any Δ consecutive layers of the temporal graph is upper-bounded by ν. We show an improved algorithm to compute a Δ-temporal matching of maximum size with a running time of ΔO(ν)⋅|G| and hence provide an exponential speedup in terms of Δ.
•An exponential speedup for Temporal Matching compared to the algorithm from Mertzios et al. [STACS '20].•Representing Δ-windows in a tree structure. |
| ArticleNumber | 106181 |
| Author | Zschoche, Philipp |
| Author_xml | – sequence: 1 givenname: Philipp surname: Zschoche fullname: Zschoche, Philipp email: zschoche@tu-berlin.de organization: Technische Universität Berlin, Faculty IV, Algorithmics and Computational Complexity, Berlin, Germany |
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| Cites_doi | 10.1016/j.dam.2021.03.014 10.1016/j.jcss.2019.07.006 10.1016/j.jcss.2019.08.002 10.1145/2886094 10.1109/TKDE.2016.2594065 10.1016/j.tcs.2021.04.002 10.1016/j.tcs.2019.03.031 10.1016/j.tcs.2019.03.026 10.1007/s00453-021-00831-w |
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| SubjectTerms | Graph algorithms Parameterized algorithms Temporal graphs Δ-windows |
| Title | A faster parameterized algorithm for temporal matching |
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