@inproceedings{436d90d1bc3f4d00a5e37f78fe67573c,
title = "Total Matching and Subdeterminants",
abstract = "In the total matching problem, one is given a graph G with weights on the vertices and edges. The goal is to find a maximum weight set of vertices and edges that is the non-incident union of a stable set and a matching. We consider the natural formulation of the problem as an integer program (IP), with variables corresponding to vertices and edges. Let M=M(G) denote the constraint matrix of this IP. We define Δ(G) as the maximum absolute value of the determinant of a square submatrix of M. We show that the total matching problem can be solved in strongly polynomial time provided Δ(G)≤Δ for some constant Δ∈Z≥1. We also show that the problem of computing Δ(G) admits an FPT algorithm. We also establish further results on Δ(G) when G is a forest.",
author = "Luca Ferrarini and Samuel Fiorini and Stefan Kober and Yelena Yuditsky",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.; 8th International Symposium on Combinatorial Optimization, ISCO 2024 ; Conference date: 22-05-2024 Through 24-05-2024",
year = "2024",
month = jan,
day = "1",
doi = "10.1007/978-3-031-60924-4_15",
language = "English",
isbn = "9783031609237",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "192--204",
editor = "Amitabh Basu and Mahjoub, {Ali Ridha} and Mahjoub, {Ali Ridha} and {Salazar Gonz{\'a}lez}, {Juan Jos{\'e}}",
booktitle = "Combinatorial Optimization - 8th International Symposium, ISCO 2024, Revised Selected Papers",
address = "Germany",
}