Hierarchical b-Matching
Yükleniyor...
Dosyalar
Tarih
2021
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer Science and Business Media Deutschland GmbH
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
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’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.
Açıklama
Anahtar Kelimeler
b-matching, Matching, Matroids, Combinatorial mathematics, NP-hard, Polynomial approximation, Cardinalities, Disjoint subsets, Matching problems, Maximum matchings, Polynomial-time algorithms, Pseudopolynomial algorithms, Second level, Sub-problems, Set theory
Kaynak
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
WoS Q Değeri
Q4
Scopus Q Değeri
Q3
Cilt
12607
Sayı
Künye
Emek, Y., Kutten, S., Shalom, M. & Zaks, S. (2021). Hierarchical b-Matching. Paper presented at the Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 12607, 189-202. doi:10.1007/978-3-030-67731-2_14
