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 language | English |
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Title of host publication | Proceedings - 2024 IEEE 65th Annual Symposium on Foundations of Computer Science, FOCS 2024 |
Publisher | IEEE Computer Society |
Pages | 1610-1620 |
Number of pages | 11 |
ISBN (Electronic) | 9798331516741 |
DOIs | |
Publication status | Published - 1 Jan 2024 |
Event | 65th IEEE Annual Symposium on Foundations of Computer Science 2024 - voco Chicago Downtown, Chicago, United States Duration: 27 Oct 2024 → 30 Oct 2024 https://focs.computer.org/2024/ |
Publication series
Series | Annual IEEE Symposium on Foundations of Computer Science |
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ISSN | 0272-5428 |
Conference
Conference | 65th IEEE Annual Symposium on Foundations of Computer Science 2024 |
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Abbreviated title | FOCS 2024 |
Country/Territory | United States |
City | Chicago |
Period | 27/10/24 → 30/10/24 |
Internet address |
Keywords
- integer linear programming
- matroid basis
- polyhedral combinatorics