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An EPTAS for Budgeted Matching and Budgeted Matroid Intersection via Representative Sets

Authors Ilan Doron-Arad, Ariel Kulik, Hadas Shachnai

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Author Details

Ilan Doron-Arad
  • Computer Science Department, Technion, Haifa, Israel
Ariel Kulik
  • CISPA Helmholtz Center for Information Security, Saarbrücken, Germany
Hadas Shachnai
  • Computer Science Department, Technion, Haifa, Israel

Funding

  • Kulik, Ariel: Research supported by the European Reseach Concil (ERC) consolidator grant no. 725978 SYSTEMATICGRAPH.

Acknowledgements

We thank an anonymous reviewer for pointing us to the work of Huang and Ward [Huang and Ward, 2020], and for other helpful comments and suggestions.

Cite AsGet BibTex

Ilan Doron-Arad, Ariel Kulik, and Hadas Shachnai. An EPTAS for Budgeted Matching and Budgeted Matroid Intersection via Representative Sets. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 49:1-49:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ICALP.2023.49

Abstract

We study the budgeted versions of the well known matching and matroid intersection problems. While both problems admit a polynomial-time approximation scheme (PTAS) [Berger et al. (Math. Programming, 2011), Chekuri, Vondrák and Zenklusen (SODA 2011)], it has been an intriguing open question whether these problems admit a fully PTAS (FPTAS), or even an efficient PTAS (EPTAS). In this paper we answer the second part of this question affirmatively, by presenting an EPTAS for budgeted matching and budgeted matroid intersection. A main component of our scheme is a construction of representative sets for desired solutions, whose cardinality depends only on ε, the accuracy parameter. Thus, enumerating over solutions within a representative set leads to an EPTAS. This crucially distinguishes our algorithms from previous approaches, which rely on exhaustive enumeration over the solution set.

Subject Classification

ACM Subject Classification
  • Theory of computation
Keywords
  • budgeted matching
  • budgeted matroid intersection
  • efficient polynomial-time approximation scheme

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