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A generalization of Hungarian method and Hall's theorem with applications in wireless sensor networksBokal, Drago, 1978- ; Brešar, Boštjan ; Jerebic, JanjaIn this paper, we consider various problems concerning quasi-matchings and semi-matchings in bipartite graphs, which generalize the classical problem of determining a perfect matching in bipartite ... graphs. We prove a generalization of Hall's marriage theorem, and present an algorithm that solves the problem of determining a lexicographically minimum ▫$g$▫-quasi-matching (that is a set ▫$F$▫ of edges in a bipartite graph such that in one set of the bipartition every vertex ▫$v$▫ has at least ▫$g(v)$▫ incident edges from ▫$F$▫, where ▫$g$▫ is a so-called need mapping, while on the other side of the bipartition the distribution of degrees with respect to ▫$F$▫ is lexicographically minimum). We obtain that finding a lexicographically minimum quasi-matching is equivalent to minimizing any strictly convex function on the degrees of the A-side of a quasi-matching and use this fact to prove a more general statement: the optima of any component-based strictly convex cost function on any subset of ▫$L_1$▫-sphere in ▫${\mathbb N}^n$▫ are precisely the lexicographically minimal elements of this subset. We also present an application in designing optimal CDMA-based wireless sensor networks.Source: Discrete applied mathematics. - ISSN 0166-218X (Vol. 160, iss. 4-5, 2012, str. 460-470)Type of material - article, component partPublish date - 2012Language - englishCOBISS.SI-ID - 16191577
Author
Bokal, Drago, 1978- |
Brešar, Boštjan |
Jerebic, Janja
Topics
matematika |
teorija grafov |
prirejanje |
kvazi prirejanje |
polprirejanje |
tok |
madžarska metoda |
mathematics |
graph theory |
matching |
quasi-matching |
semi-matching |
flow |
Hungarian method |
augmenting path
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Bokal, Drago, 1978- | 22402 |
Brešar, Boštjan | 17005 |
Jerebic, Janja | 24751 |
Source: Personal bibliographies
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