2 Search Results for "Doron-Arad, Ilan"

Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.22
An AFPTAS for Bin Packing with Partition Matroid via a New Method for LP Rounding

Authors: Ilan Doron-Arad, Ariel Kulik, and Hadas Shachnai

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract
We consider the Bin Packing problem with a partition matroid constraint. The input is a set of items of sizes in [0,1], and a partition matroid over the items. The goal is to pack the items in a minimum number of unit-size bins, such that each bin forms an independent set in the matroid. This variant of classic Bin Packing has natural applications in secure storage on the Cloud, as well as in equitable scheduling and clustering with fairness constraints. Our main result is an asymptotic fully polynomial-time approximation scheme (AFPTAS) for Bin Packing with a partition matroid constraint. This scheme generalizes the known AFPTAS for Bin Packing with Cardinality Constraints and improves the existing asymptotic polynomial-time approximation scheme (APTAS) for Group Bin Packing, which are both special cases of Bin Packing with partition matroid. We derive the scheme via a new method for rounding a (fractional) solution for a configuration-LP. Our method uses this solution to obtain prototypes, in which items are interpreted as placeholders for other items, and applies fractional grouping to modify a fractional solution (prototype) into one having desired integrality properties.
Cite as

Ilan Doron-Arad, Ariel Kulik, and Hadas Shachnai. An AFPTAS for Bin Packing with Partition Matroid via a New Method for LP Rounding. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 22:1-22:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{doronarad_et_al:LIPIcs.APPROX/RANDOM.2023.22,
  author =	{Doron-Arad, Ilan and Kulik, Ariel and Shachnai, Hadas},
  title =	{{An AFPTAS for Bin Packing with Partition Matroid via a New Method for LP Rounding}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{22:1--22:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.22},
  URN =		{urn:nbn:de:0030-drops-188470},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.22},
  annote =	{Keywords: bin packing, partition-matroid, AFPTAS, LP-rounding}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.49
An EPTAS for Budgeted Matching and Budgeted Matroid Intersection via Representative Sets

Authors: Ilan Doron-Arad, Ariel Kulik, and Hadas Shachnai

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

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.
Cite as

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)

Copy BibTex To Clipboard

@InProceedings{doronarad_et_al:LIPIcs.ICALP.2023.49,
  author =	{Doron-Arad, Ilan and Kulik, Ariel and Shachnai, Hadas},
  title =	{{An EPTAS for Budgeted Matching and Budgeted Matroid Intersection via Representative Sets}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{49:1--49:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.49},
  URN =		{urn:nbn:de:0030-drops-181018},
  doi =		{10.4230/LIPIcs.ICALP.2023.49},
  annote =	{Keywords: budgeted matching, budgeted matroid intersection, efficient polynomial-time approximation scheme}
}
  • Refine by Author
  • 2 Doron-Arad, Ilan
  • 2 Kulik, Ariel
  • 2 Shachnai, Hadas

  • Refine by Classification
  • 2 Theory of computation

  • Refine by Keyword
  • 1 AFPTAS
  • 1 LP-rounding
  • 1 bin packing
  • 1 budgeted matching
  • 1 budgeted matroid intersection
  • Show More...

  • Refine by Type
  • 2 document

  • Refine by Publication Year
  • 2 2023

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023 Schloss Dagstuhl - LZI GmbH Imprint Privacy Contact