@inproceedings{617c577741404ab3b9b03aaa5e970b65,
title = "Hierarchical b-Matching",
abstract = "A matching of a graph is a subset of edges no two of which share a common vertex, and a maximum matching is a matching of maximum cardinality. In a b-matching every vertex v has an associated bound bv, and a maximum b-matching is a maximum set of edges, such that every vertex v appears in at most bv of them. We study an extension of this problem, termed Hierarchical b-Matching. In this extension, the vertices are arranged in a hierarchical manner. At the first level the vertices are partitioned into disjoint subsets, with a given bound for each subset. At the second level the set of these subsets is again partitioned into disjoint subsets, with a given bound for each subset, and so on. We seek for a maximum set of edges, that obey all bounds (that is, no vertex v participates in more than bv edges, then all the vertices in one subset do not participate in more that subset{\textquoteright}s bound of edges, and so on hierarchically). This is a sub-problem of the matroid matching problem which is NP -hard in general. It corresponds to the special case where the matroid is restricted to be laminar and the weights are unity. A pseudo-polynomial algorithm for the weighted laminar matroid matching problem is presented in [8]. We propose a polynomial-time algorithm for Hierarchical b-matching, i.e. the unweighted laminar matroid matching problem, and discuss how our techniques can possibly be generalized to the weighted case.",
keywords = "Matching, Matroids, b-matching",
author = "Yuval Emek and Shay Kutten and Mordechai Shalom and Shmuel Zaks",
note = "Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.; 47th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2021 ; Conference date: 25-01-2021 Through 29-01-2021",
year = "2021",
doi = "10.1007/978-3-030-67731-2_14",
language = "الإنجليزيّة",
isbn = "9783030677305",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "189--202",
editor = "Tom{\'a}{\v s} Bure{\v s} and Riccardo Dondi and Johann Gamper and Giovanna Guerrini and Tomasz Jurdzinski and Claus Pahl and Florian Sikora and Wong, {Prudence W.}",
booktitle = "SOFSEM 2021",
address = "ألمانيا",
}