Sensitivity, Proximity and FPT Algorithms for Exact Matroid Problems

Friedrich Eisenbrand; Lars Rohwedder; Karol Wegrzycki

doi:10.1109/FOCS61266.2024.00100

Sensitivity, Proximity and FPT Algorithms for Exact Matroid Problems

Friedrich Eisenbrand^*, Lars Rohwedder, Karol Wegrzycki

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-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 language	English
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	https://doi.org/10.1109/FOCS61266.2024.00100
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
ISSN	0272-5428

Conference

Conference	65th IEEE Annual Symposium on Foundations of Computer Science 2024
Abbreviated title	FOCS 2024
Country/Territory	United States
City	Chicago
Period	27/10/24 → 30/10/24
Internet address	https://focs.computer.org/2024/

Keywords

integer linear programming
matroid basis
polyhedral combinatorics

Access to Document

10.1109/FOCS61266.2024.00100

Cite this

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title = "Sensitivity, Proximity and FPT Algorithms for Exact Matroid Problems",

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.",

keywords = "integer linear programming, matroid basis, polyhedral combinatorics",

author = "Friedrich Eisenbrand and Lars Rohwedder and Karol Wegrzycki",

note = "Funding Information: The second author was supported by Dutch Research Council (NWO) project \textbackslash{}{"}The Twilight Zone of Efficiency: Optimality of Quasi-Polynomial Time Algorithms\textbackslash{}{"} [grant number OCEN.W.21.268]. The third author was supported by the project TIPEA that has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement No. 850979). data source: no data used ; 65th IEEE Annual Symposium on Foundations of Computer Science 2024, FOCS 2024 ; Conference date: 27-10-2024 Through 30-10-2024",

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month = jan,

day = "1",

doi = "10.1109/FOCS61266.2024.00100",

language = "English",

series = "Annual IEEE Symposium on Foundations of Computer Science",

publisher = "IEEE Computer Society",

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booktitle = "Proceedings - 2024 IEEE 65th Annual Symposium on Foundations of Computer Science, FOCS 2024",

address = "United States",

url = "https://focs.computer.org/2024/",

}

Eisenbrand, F, Rohwedder, L & Wegrzycki, K 2024, Sensitivity, Proximity and FPT Algorithms for Exact Matroid Problems. in Proceedings - 2024 IEEE 65th Annual Symposium on Foundations of Computer Science, FOCS 2024. IEEE Computer Society, Annual IEEE Symposium on Foundations of Computer Science, pp. 1610-1620, 65th IEEE Annual Symposium on Foundations of Computer Science 2024, Chicago, Illinois, United States, 27/10/24. https://doi.org/10.1109/FOCS61266.2024.00100

Sensitivity, Proximity and FPT Algorithms for Exact Matroid Problems. / Eisenbrand, Friedrich; Rohwedder, Lars; Wegrzycki, Karol.
Proceedings - 2024 IEEE 65th Annual Symposium on Foundations of Computer Science, FOCS 2024. IEEE Computer Society, 2024. p. 1610-1620 (Annual IEEE Symposium on Foundations of Computer Science).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

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AU - Rohwedder, Lars

AU - Wegrzycki, Karol

N1 - Funding Information: The second author was supported by Dutch Research Council (NWO) project \"The Twilight Zone of Efficiency: Optimality of Quasi-Polynomial Time Algorithms\" [grant number OCEN.W.21.268]. The third author was supported by the project TIPEA that has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement No. 850979). data source: no data used

PY - 2024/1/1

Y1 - 2024/1/1

N2 - 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.

AB - 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.

KW - integer linear programming

KW - matroid basis

KW - polyhedral combinatorics

U2 - 10.1109/FOCS61266.2024.00100

DO - 10.1109/FOCS61266.2024.00100

M3 - Conference article in proceeding

T3 - Annual IEEE Symposium on Foundations of Computer Science

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EP - 1620

BT - Proceedings - 2024 IEEE 65th Annual Symposium on Foundations of Computer Science, FOCS 2024

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T2 - 65th IEEE Annual Symposium on Foundations of Computer Science 2024

Y2 - 27 October 2024 through 30 October 2024

ER -

Sensitivity, Proximity and FPT Algorithms for Exact Matroid Problems

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