• Treffer 1 von 1
Zurück zur Trefferliste

Linear-Time Algorithms for Maximum-Weight Induced Matchings and Minimum Chain Covers in Convex Bipartite Graphs

Zitieren Sie bitte immer diese URN: urn:nbn:de:bvb:20-opus-267876
  • A bipartite graph G=(U,V,E) is convex if the vertices in V can be linearly ordered such that for each vertex u∈U, the neighbors of u are consecutive in the ordering of V. An induced matching H of G is a matching for which no edge of E connects endpoints of two different edges of H. We show that in a convex bipartite graph with n vertices and m weighted edges, an induced matching of maximum total weight can be computed in O(n+m) time. An unweighted convex bipartite graph has a representation of size O(n) that records for each vertex u∈U theA bipartite graph G=(U,V,E) is convex if the vertices in V can be linearly ordered such that for each vertex u∈U, the neighbors of u are consecutive in the ordering of V. An induced matching H of G is a matching for which no edge of E connects endpoints of two different edges of H. We show that in a convex bipartite graph with n vertices and m weighted edges, an induced matching of maximum total weight can be computed in O(n+m) time. An unweighted convex bipartite graph has a representation of size O(n) that records for each vertex u∈U the first and last neighbor in the ordering of V. Given such a compact representation, we compute an induced matching of maximum cardinality in O(n) time. In convex bipartite graphs, maximum-cardinality induced matchings are dual to minimum chain covers. A chain cover is a covering of the edge set by chain subgraphs, that is, subgraphs that do not contain induced matchings of more than one edge. Given a compact representation, we compute a representation of a minimum chain cover in O(n) time. If no compact representation is given, the cover can be computed in O(n+m) time. All of our algorithms achieve optimal linear running time for the respective problem and model, and they improve and generalize the previous results in several ways: The best algorithms for the unweighted problem versions had a running time of O(n\(^{2}\)) (Brandstädt et al. in Theor. Comput. Sci. 381(1–3):260–265, 2007. https://doi.org/10.1016/j.tcs.2007.04.006). The weighted case has not been considered before.zeige mehrzeige weniger

Volltext Dateien herunterladen

Metadaten exportieren

Weitere Dienste

Teilen auf Twitter Suche bei Google Scholar Statistik - Anzahl der Zugriffe auf das Dokument
Metadaten
Autor(en): Boris Klemz, Günter Rote
URN:urn:nbn:de:bvb:20-opus-267876
Dokumentart:Artikel / Aufsatz in einer Zeitschrift
Institute der Universität:Fakultät für Mathematik und Informatik / Institut für Informatik
Sprache der Veröffentlichung:Englisch
Titel des übergeordneten Werkes / der Zeitschrift (Englisch):Algorithmica
ISSN:1432-0541
Erscheinungsjahr:2022
Band / Jahrgang:84
Heft / Ausgabe:4
Seitenangabe:1064–1080
Originalveröffentlichung / Quelle:Algorithmica 2022, 84(4):1064–1080. DOI: 10.1007/s00453-021-00904-w
DOI:https://doi.org/10.1007/s00453-021-00904-w
Allgemeine fachliche Zuordnung (DDC-Klassifikation):0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
Freie Schlagwort(e):certifying algorithm; chain cover; convex bipartite graph; dynamic programming; graph algorithm; induced matching
Datum der Freischaltung:07.06.2022
Lizenz (Deutsch):License LogoCC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International