Sensitivity, Proximity and FPT Algorithms for Exact Matroid Problems

Friedrich Eisenbrand, Lars Rohwedder, Karol Wegrzycki

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

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 -?, ·, ? or more generally m-dimensional vectors of such discrete values. We resolve the parameterized complexity completely, by presenting an FPT algorithm parameterized by ? and m for arbitrary matroids. Prior to our work, no such algorithms were known even when weights are in 0,1, or arbitrary ? 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.
Original languageEnglish
Title of host publicationProceedings - 2024 IEEE 65th Annual Symposium on Foundations of Computer Science, FOCS 2024
PublisherIEEE Computer Society
Pages1610-1620
Number of pages11
ISBN (Electronic)9798331516741
DOIs
Publication statusPublished - 1 Jan 2024
Event65th IEEE Annual Symposium on Foundations of Computer Science 2024 - voco Chicago Downtown, Chicago, United States
Duration: 27 Oct 202430 Oct 2024
https://focs.computer.org/2024/

Publication series

SeriesAnnual IEEE Symposium on Foundations of Computer Science
ISSN0272-5428

Conference

Conference65th IEEE Annual Symposium on Foundations of Computer Science 2024
Abbreviated titleFOCS 2024
Country/TerritoryUnited States
CityChicago
Period27/10/2430/10/24
Internet address

Keywords

  • integer linear programming
  • matroid basis
  • polyhedral combinatorics

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