Maximal rank in matrix spaces via graph matchings
نویسندگان
چکیده
منابع مشابه
Dynamic Rank-Maximal Matchings
We consider the problem of matching applicants to posts where applicants have preferences over posts. Thus the input to our problem is a bipartite graph G = (A ∪ P , E), where A denotes a set of applicants, P is a set of posts, and there are ranks on edges which denote the preferences of applicants over posts. A matching M in G is called rank-maximal if it matches the maximum number of applican...
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Let $S= \{e_1,\,e_2, \ldots,\,e_m\}$ be an ordered subset of edges of a connected graph $G$. The edge $S$-representation of an edge set $M\subseteq E(G)$ with respect to $S$ is the vector $r_e(M|S) = (d_1,\,d_2,\ldots,\,d_m)$, where $d_i=1$ if $e_i\in M$ and $d_i=0$ otherwise, for each $i\in\{1,\ldots , k\}$. We say $S$ is a global forcing set for maximal matchings of $G$ if $...
متن کاملRank-Maximal Matchings - Structure and Algorithms
Let G = (A ∪ P , E) be a bipartite graph where A denotes a set of agents, P denotes a set of posts and ranks on the edges denote preferences of the agents over posts. A matching M in G is rank-maximal if it matches the maximum number of applicants to their top-rank post, subject to this, the maximum number of applicants to their second rank
متن کاملThe Dynamics of Rank-Maximal and Popular Matchings
Given a bipartite graph, where the two sets of vertices are applicants and posts and ranks on the edges represent preferences of applicants over posts, a rank-maximal matching is one in which the maximum number of applicants is matched to their rank one posts and subject to this condition, the maximum number of applicants is matched to their rank two posts, and so on. A rank-maximal matching ca...
متن کاملEfficient Algorithms for Weighted Rank-Maximal Matchings and Related Problems
We consider the problem of designing efficient algorithms for computing certain matchings in a bipartite graph G = (A ∪ P, E), with a partition of the edge set as E = E1 ∪̇ E2 . . . ∪̇ Er. A matching is a set of (a, p) pairs, a ∈ A, p ∈ P such that each a and each p appears in at most one pair. We first consider the popular matching problem; an O(m √ n) algorithm to solve the popular matching pro...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2017
ISSN: 0024-3795
DOI: 10.1016/j.laa.2017.04.016