Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6872600 | Discrete Applied Mathematics | 2012 | 11 Pages |
Abstract
In 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 L1-sphere in Nn are precisely the lexicographically minimal elements of this subset. We also present an application in designing optimal CDMA-based wireless sensor networks.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Drago Bokal, Boštjan Brešar, Janja Jerebic,