par Ferrarini, Luca;Fiorini, Samuel 
;Kober, Stefan ;Yuditsky, Yelena
Référence Lecture notes in computer science, 14594 LNCS, page (192-204)
Publication Publié, 2024-01-01
;Kober, Stefan ;Yuditsky, Yelena Référence Lecture notes in computer science, 14594 LNCS, page (192-204)
Publication Publié, 2024-01-01
Article révisé par les pairs
| Résumé : | 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. |
