Abstract
The k-cardinality assignment (k-assignment, for short) problem asks for finding a minimal (maximal) weight of a matching of cardinality k in a weighted bipartite graph Kn,n , k ≤ n. Here we are interested in computing the sequence of all k-assignments, k=1,...,n. By applying the algorithm of Gassner and Klinz (2010) for the parametric assignment problem one can compute in time O(n3) the set of k-assignments for those integers k≤n which refer to essential terms of the full characteristic maxpolynomial χW(x) of the corresponding max-plus weight matrix W. We show that χW(x) is in full canonical form, which implies that the remaining k-assignments refer to semi-essential terms of χW(x). This property enables us to efficiently compute in time O(n2) all the remaining k-assignments out of the already computed essential k-assignments. It follows that time complexity for computing the sequence of all k-cardinality assignments is O(n3) ,which is the best known time for this problem.}
Originalsprache | englisch |
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Seiten (von - bis) | 1265-1283 |
Seitenumfang | 19 |
Fachzeitschrift | Journal of Combinatorial Optimization |
Jahrgang | 44 |
Ausgabenummer | 2 |
Frühes Online-Datum | 24 Juli 2022 |
DOIs | |
Publikationsstatus | Veröffentlicht - Sept. 2022 |
ASJC Scopus subject areas
- Steuerung und Optimierung
- Angewandte Mathematik
- Diskrete Mathematik und Kombinatorik
- Angewandte Informatik
- Theoretische Informatik und Mathematik