2026-07-21T12:35:04Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:19359 2024-12-04T07:19:40Z ddc:004 open_access

A Strongly Polynomial-Time Algorithm for Weighted General Factors with Three Feasible Degrees Shao, Shuai Živný, Stanislav matchings factors edge constraint satisfaction problems terminal backup problem delta matroids General factors are a generalization of matchings. Given a graph G with a set π(v) of feasible degrees, called a degree constraint, for each vertex v of G, the general factor problem is to find a (spanning) subgraph F of G such that deg_F(v) ∈ π(v) for every v of G. When all degree constraints are symmetric Δ-matroids, the problem is solvable in polynomial time. The weighted general factor problem is to find a general factor of the maximum total weight in an edge-weighted graph. Strongly polynomial-time algorithms are only known for weighted general factor problems that are reducible to the weighted matching problem by gadget constructions. In this paper, we present a strongly polynomial-time algorithm for a type of weighted general factor problems with real-valued edge weights that is provably not reducible to the weighted matching problem by gadget constructions. As an application, we obtain a strongly polynomial-time algorithm for the terminal backup problem by reducing it to the weighted general factor problem. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Shuai Shao and Stanislav Živný 2023 Is Part Of LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2023.57 urn:nbn:de:0030-drops-193597 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.57 eng https://creativecommons.org/licenses/by/4.0/legalcode