Year: 2022
Type: preprint
Abstract: Given a graph $G=(V,E)$ with costs on its edges, the minimum-cost edge cover problem consists of finding a subset of $E$ covering all vertices in $V$ at minimum cost. If $G$ is bipartite, this problem can be solved in time $O(|V|^3)$ via a well-known reduction to a maximum-cost matching problem on $G$. If in addition $V$ is a set of points on the Euclidean line, Collanino et al. showed that the problem can be solved in time $O(|V| \log |V|)$ and asked whether it can be solved in time $o(|V|^3)$ if $V$ is a set of points on the Euclidean plane. We answer this in the affirmative, giving an $O(|V|^{2.5} \log |V|)$ algorithm based on the Hungarian method using weighted Voronoi diagrams. We also propose some 2-approximation algorithms and give experimental results of our implementations.
Source: arXiv (Cornell University)
Authors: Castro, Rodrigo A., Díaz-Báñez, José M., Heredia, Marco A., Urrutia, Jorge, Ventura, Inmaculada, Zaragoza, Francisco J.
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4286225550