Search Results

Question: what is known about the algorithmic aspects of optimally matching a set $\mathcal{P} = \prod\limits_{i=1}^n \left(1,\,\cdots,\,k_i\right)$ of grid-points to a set of $\prod\limits_{i=1}^nk_ …

Question: are there any algorithms, resp. what can be recommended, for calculating perfect matchings with the property that the variance of their edge's weights is minimal?

This is a followup to my question How does the complexity of calculating the Permanent imply the NP completeness of directed 3-cycle cover? Question: who contributed problem [GT13] PARTITION INTO HAM …

A directed cycle-cover of a digraph $D$ is in the sense of this post equivalent to a perfect matching in the related undirected biadjacency graph $B$ in which the edges connect a vertex $u$ of $D$ in …

The subject of the paywalled article The minimum cost perfect matching problem with conflict pair constraints (MCPMPC) are perfect matchings of minimum cost that do not contain certain pairs of edges; …

This is a follow-up question to Minimum-weight disjoint union of perfect matchings: let $G$ be a complete symmetric graph with $2n$ vertices, whose edges are mapped to their weights by $\omega()$ and …

Question: what is known about minimum/maximum weight perfect matchings in magic squares with or without special properties like e.g. being pandiagonal? I am especially interested minimal/maximal cel …

Given a complete weighted graph $G(V,E),\ |V|=2n$, calculating a minimum weight matching with $n-k$ edges can be reduced to calculating a perfect matching in $H(V+U,E+F),\ |U|=2k,\ F=(u\in U,v\in V),\ …

A fairly wellknown heuristic for TSP that is based on matching is described in the 2003 paper Match twice and stitch: a new TSP tour construction heuristic by Andrew B. Kahng and Sherief Reda. Its bas …

Question: what can be said about the existence of $2k$ regular graphs, $1\lt k$ that have a $1$-factor and a $2$-factor? Provided their existence, what is/are the smallest for $k$? The graphs must b …

Question: What can be recommended for finding optimal perfect matchings in large bipartite graphs with small vertex degree if the edge-weights are positive real values? I am looking for algor …

The subject of this question are perfect matchings of a complete undirected graph $G(V,E), n:=\mathrm{card}(V)=2k$, without self-loops or parallel edges and $n=2k$ vertices. The objective is to determ …

Is there a sound proof of or a counter example to the following conjecture: if $\boldsymbol{A}^T=\boldsymbol{A}$ is the cost-matrix of a bipartite assignment problem with unique optimal assignment, t …

as already mentioned in the comments, that is answered by Alexander Schrijver in his publication "Counting 1-factors in regular bipartite graphs": any $k$-regular bipartite graph with $2n$ vertices h …

pyMCFSimplex seems to best fit my needs. "It is a free Python port of a Python Wrapper for MCFSimplex. pyMCFimplex is a Python-Wrapper for the C++ MCFSimplex Solver Class from the Operations Research …