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- W2950758304 abstract "Given a graph $G=(V,E)$ and for each vertex $v in V$ a subset $B(v)$ of the set ${0,1,ldots, d_G(v)}$ a $B$-matching of $G$ is any set $F subseteq E$ such that $d_F(v) in B(v)$ for each vertex $v$. The general matching problem asks the existence of a $B$-matching in a given graph. A set $B(v)$ is said to have a {em gap of length} $p$ if there exists a number $k in B(v)$ such that $k+1, ldots, k+p notin B(v)$ and $k+p+1 in B(v)$. Without any restrictions the general matching problem is NP-complete. However, if no set $B(v)$ contains a gap of length greater than $1$, then the problem can be solved in polynomial time and Cornuejols cite{Cor} presented an algorithm for finding a $B$-matching, if it exists. In this paper we consider a version of the general matching problem, in which we are interested in finding a $B$-matching having a maximum (or minimum) number of edges. We present the first polynomial time algorithm for the maximum weight $B$-matching for the case when no set $B(v)$ contains a gap of length greater than $1$." @default.
- W2950758304 created "2019-06-27" @default.
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- W2950758304 date "2017-06-22" @default.
- W2950758304 modified "2023-09-26" @default.
- W2950758304 title "Optimal General Matchings." @default.
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