Work

Sensitivity, Proximity and FPT Algorithms for Exact Matroid Problems

Year: 2024

Type: conference-paper

Abstract: We consider the problem of finding a basis of a matroid with weight exactly equal to a given target. Here weights can be discrete values from$\{-\Delta,\ \ldots,\ \Delta\}$or more generally m-dimensional vectors of such discrete values. We resolve the parameterized complexity completely, by presenting an FPT algorithm parameterized by$\Delta$and$m$for arbitrary matroids. Prior to our work, no such algorithms were known even when weights are in$\{0,1\}$, or arbitrary$\Delta$and$m=1$. Our main technical contributions are new proximity and sensitivity bounds for matroid problems, independent of the number of elements. These bounds imply FPT algorithms via matroid intersection.

Source: Annual Symposium on Foundations of Computer Science

DOI: 10.1109/focs61266.2024.00100

Authors: Friedrich Eisenbrand, Lars Rohwedder, Karol Węgrzycki

Institutions: École Polytechnique Fédérale de Lausanne, Maastricht University, Max Planck Institute for Informatics, Saarland University

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Nederlandse Organisatie voor Wetenschappelijk Onderzoek, Universität des Saarlandes, H2020 European Research Council

Award: Technology Transfer between Integer Programming and Efficient Algorithms