3 Search Results for "Fairstein, Yaron"


Document
APPROX
General Knapsack Problems in a Dynamic Setting

Authors: Yaron Fairstein, Ariel Kulik, Joseph (Seffi) Naor, and Danny Raz

Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)


Abstract
The world is dynamic and changes over time, thus any optimization problem used to model real life problems must address this dynamic nature, taking into account the cost of changes to a solution over time. The multistage model was introduced with this goal in mind. In this model we are given a series of instances of an optimization problem, corresponding to different times, and a solution is provided for each instance. The strive for obtaining near-optimal solutions for each instance on one hand, while maintaining similar solutions for consecutive time units on the other hand, is quantified and integrated into the objective function. In this paper we consider the Generalized Multistage d-Knapsack problem, a generalization of the multistage variants of the Multiple Knapsack problem, as well as the d-Dimensional Knapsack problem. We present a PTAS for Generalized Multistage d-Knapsack.

Cite as

Yaron Fairstein, Ariel Kulik, Joseph (Seffi) Naor, and Danny Raz. General Knapsack Problems in a Dynamic Setting. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{fairstein_et_al:LIPIcs.APPROX/RANDOM.2021.15,
  author =	{Fairstein, Yaron and Kulik, Ariel and Naor, Joseph (Seffi) and Raz, Danny},
  title =	{{General Knapsack Problems in a Dynamic Setting}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.15},
  URN =		{urn:nbn:de:0030-drops-147081},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.15},
  annote =	{Keywords: Multistage, Multiple-Knapsacks, Multidimensional Knapsack}
}
Document
Modular and Submodular Optimization with Multiple Knapsack Constraints via Fractional Grouping

Authors: Yaron Fairstein, Ariel Kulik, and Hadas Shachnai

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)


Abstract
A multiple knapsack constraint over a set of items is defined by a set of bins of arbitrary capacities, and a weight for each of the items. An assignment for the constraint is an allocation of subsets of items to the bins which adheres to bin capacities. In this paper we present a unified algorithm that yields efficient approximations for a wide class of submodular and modular optimization problems involving multiple knapsack constraints. One notable example is a polynomial time approximation scheme for Multiple-Choice Multiple Knapsack, improving upon the best known ratio of 2. Another example is Non-monotone Submodular Multiple Knapsack, for which we obtain a (0.385-ε)-approximation, matching the best known ratio for a single knapsack constraint. The robustness of our algorithm is achieved by applying a novel fractional variant of the classical linear grouping technique, which is of independent interest.

Cite as

Yaron Fairstein, Ariel Kulik, and Hadas Shachnai. Modular and Submodular Optimization with Multiple Knapsack Constraints via Fractional Grouping. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 41:1-41:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{fairstein_et_al:LIPIcs.ESA.2021.41,
  author =	{Fairstein, Yaron and Kulik, Ariel and Shachnai, Hadas},
  title =	{{Modular and Submodular Optimization with Multiple Knapsack Constraints via Fractional Grouping}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{41:1--41:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.41},
  URN =		{urn:nbn:de:0030-drops-146229},
  doi =		{10.4230/LIPIcs.ESA.2021.41},
  annote =	{Keywords: Sumodular Optimization, Multiple Knapsack, Randomized Rounding, Linear Grouping, Multiple Choice Multiple Knapsack}
}
Document
A (1-e^{-1}-ε)-Approximation for the Monotone Submodular Multiple Knapsack Problem

Authors: Yaron Fairstein, Ariel Kulik, Joseph (Seffi) Naor, Danny Raz, and Hadas Shachnai

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)


Abstract
We study the problem of maximizing a monotone submodular function subject to a Multiple Knapsack constraint (SMKP). The input is a set I of items, each associated with a non-negative weight, and a set of bins having arbitrary capacities. Also, we are given a submodular, monotone and non-negative function f over subsets of the items. The objective is to find a subset of items A ⊆ I and a packing of these items in the bins, such that f(A) is maximized. SMKP is a natural extension of both Multiple Knapsack and the problem of monotone submodular maximization subject to a knapsack constraint. Our main result is a nearly optimal polynomial time (1-e^{-1}-ε)-approximation algorithm for the problem, for any ε > 0. Our algorithm relies on a refined analysis of techniques for constrained submodular optimization combined with sophisticated application of tools used in the development of approximation schemes for packing problems.

Cite as

Yaron Fairstein, Ariel Kulik, Joseph (Seffi) Naor, Danny Raz, and Hadas Shachnai. A (1-e^{-1}-ε)-Approximation for the Monotone Submodular Multiple Knapsack Problem. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 44:1-44:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{fairstein_et_al:LIPIcs.ESA.2020.44,
  author =	{Fairstein, Yaron and Kulik, Ariel and Naor, Joseph (Seffi) and Raz, Danny and Shachnai, Hadas},
  title =	{{A (1-e^\{-1\}-\epsilon)-Approximation for the Monotone Submodular Multiple Knapsack Problem}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{44:1--44:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.44},
  URN =		{urn:nbn:de:0030-drops-129107},
  doi =		{10.4230/LIPIcs.ESA.2020.44},
  annote =	{Keywords: Sumodular Optimization, Multiple Knapsack, Randomized Rounding}
}
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