Academic Journal
Linear-Time Algorithms for Maximum-Weight Induced Matchings and Minimum Chain Covers in Convex Bipartite Graphs
| Τίτλος: | Linear-Time Algorithms for Maximum-Weight Induced Matchings and Minimum Chain Covers in Convex Bipartite Graphs |
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| Συγγραφείς: | Klemz, Boris, Rote, Günter |
| Έτος έκδοσης: | 2022 |
| Συλλογή: | FU Berlin: Refubium |
| Θεματικοί όροι: | Graph algorithm, Induced matching, Chain cover, Convex bipartite graph, Certifying algorithm, Dynamic programming, ddc:004 |
| Περιγραφή: | 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 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(n2) (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. |
| Τύπος εγγράφου: | article in journal/newspaper |
| Περιγραφή αρχείου: | 17 Seiten; application/pdf |
| Γλώσσα: | English |
| DOI: | 10.17169/refubium-33566 |
| DOI: | 10.1007/s00453-021-00904-w |
| Διαθεσιμότητα: | https://refubium.fu-berlin.de/handle/fub188/33847 https://doi.org/10.17169/refubium-33566 https://doi.org/10.1007/s00453-021-00904-w |
| Rights: | https://creativecommons.org/licenses/by/4.0/ |
| Αριθμός Καταχώρησης: | edsbas.D82F7DC5 |
| Βάση Δεδομένων: | BASE |
| DOI: | 10.17169/refubium-33566 |
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