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Documents authored by Naor, Joseph (Seffi)

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.57
Non-Linear Paging

Authors: Ilan Doron-Arad and Joseph (Seffi) Naor

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We formulate and study non-linear paging - a broad model of online paging where the size of subsets of pages is determined by a monotone non-linear set function of the pages. This model captures the well-studied classic weighted paging and generalized paging problems, and also submodular and supermodular paging, studied here for the first time, that have a range of applications from virtual memory to machine learning. Unlike classic paging, the cache threshold parameter k does not yield good competitive ratios for non-linear paging. Instead, we introduce a novel parameter 𝓁 that generalizes the notion of cache size to the non-linear setting. We obtain a tight deterministic 𝓁-competitive algorithm for general non-linear paging and a o(log²𝓁)-competitive lower bound for randomized algorithms. Our algorithm is based on a new generic LP for the problem that captures both submodular and supermodular paging, in contrast to LPs used for submodular cover settings. We finally focus on the supermodular paging problem, which is a variant of online set cover and online submodular cover, where sets are repeatedly requested to be removed from the cover. We obtain polylogarithmic lower and upper bounds and an offline approximation algorithm.
Cite as

Ilan Doron-Arad and Joseph (Seffi) Naor. Non-Linear Paging. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 57:1-57:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{doronarad_et_al:LIPIcs.ICALP.2024.57,
  author =	{Doron-Arad, Ilan and Naor, Joseph (Seffi)},
  title =	{{Non-Linear Paging}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{57:1--57:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.57},
  URN =		{urn:nbn:de:0030-drops-202000},
  doi =		{10.4230/LIPIcs.ICALP.2024.57},
  annote =	{Keywords: paging, competitive analysis, non-linear paging, submodular and supermodular functions}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2021.15
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.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
DOI: 10.4230/LIPIcs.ESA.2020.44
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.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}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.88
Tight Bounds for Online Weighted Tree Augmentation

Authors: Joseph (Seffi) Naor, Seeun William Umboh, and David P. Williamson

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
The Weighted Tree Augmentation problem (WTAP) is a fundamental problem in network design. In this paper, we consider this problem in the online setting. We are given an n-vertex spanning tree T and an additional set L of edges (called links) with costs. Then, terminal pairs arrive one-by-one and our task is to maintain a low-cost subset of links F such that every terminal pair that has arrived so far is 2-edge-connected in T cup F. This online problem was first studied by Gupta, Krishnaswamy and Ravi (SICOMP 2012) who used it as a subroutine for the online survivable network design problem. They gave a deterministic O(log^2 n)-competitive algorithm and showed an Omega(log n) lower bound on the competitive ratio of randomized algorithms. The case when T is a path is also interesting: it is exactly the online interval set cover problem, which also captures as a special case the parking permit problem studied by Meyerson (FOCS 2005). The contribution of this paper is to give tight results for online weighted tree and path augmentation problems. The main result of this work is a deterministic O(log n)-competitive algorithm for online WTAP, which is tight up to constant factors.
Cite as

Joseph (Seffi) Naor, Seeun William Umboh, and David P. Williamson. Tight Bounds for Online Weighted Tree Augmentation. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 88:1-88:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{naor_et_al:LIPIcs.ICALP.2019.88,
  author =	{Naor, Joseph (Seffi) and Umboh, Seeun William and Williamson, David P.},
  title =	{{Tight Bounds for Online Weighted Tree Augmentation}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{88:1--88:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.88},
  URN =		{urn:nbn:de:0030-drops-106647},
  doi =		{10.4230/LIPIcs.ICALP.2019.88},
  annote =	{Keywords: Online algorithms, competitive analysis, tree augmentation, network design}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.34
Correlated Rounding of Multiple Uniform Matroids and Multi-Label Classification

Authors: Shahar Chen, Dotan Di Castro, Zohar Karnin, Liane Lewin-Eytan, Joseph (Seffi) Naor, and Roy Schwartz

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract
We introduce correlated randomized dependent rounding where, given multiple points y^1,...,y^n in some polytope P\subseteq [0,1]^k, the goal is to simultaneously round each y^i to some integral z^i in P while preserving both marginal values and expected distances between the points. In addition to being a natural question in its own right, the correlated randomized dependent rounding problem is motivated by multi-label classification applications that arise in machine learning, e.g., classification of web pages, semantic tagging of images, and functional genomics. The results of this work can be summarized as follows: (1) we present an algorithm for solving the correlated randomized dependent rounding problem in uniform matroids while losing only a factor of O(log{k}) in the distances (k is the size of the ground set); (2) we introduce a novel multi-label classification problem, the metric multi-labeling problem, which captures the above applications. We present a (true) O(log{k})-approximation for the general case of metric multi-labeling and a tight 2-approximation for the special case where there is no limit on the number of labels that can be assigned to an object.
Cite as

Shahar Chen, Dotan Di Castro, Zohar Karnin, Liane Lewin-Eytan, Joseph (Seffi) Naor, and Roy Schwartz. Correlated Rounding of Multiple Uniform Matroids and Multi-Label Classification. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2017.34,
  author =	{Chen, Shahar and Di Castro, Dotan and Karnin, Zohar and Lewin-Eytan, Liane and Naor, Joseph (Seffi) and Schwartz, Roy},
  title =	{{Correlated Rounding of Multiple Uniform Matroids and Multi-Label Classification}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{34:1--34:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.34},
  URN =		{urn:nbn:de:0030-drops-74612},
  doi =		{10.4230/LIPIcs.ICALP.2017.34},
  annote =	{Keywords: approximation algorithms, randomized rounding, dependent rounding, metric labeling, classification}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.40
Online Semidefinite Programming

Authors: Noa Elad, Satyen Kale, and Joseph (Seffi) Naor

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
We consider semidefinite programming through the lens of online algorithms - what happens if not all input is given at once, but rather iteratively? In what way does it make sense for a semidefinite program to be revealed? We answer these questions by defining a model for online semidefinite programming. This model can be viewed as a generalization of online coveringpacking linear programs, and it also captures interesting problems from quantum information theory. We design an online algorithm for semidefinite programming, utilizing the online primaldual method, achieving a competitive ratio of O(log(n)), where n is the number of matrices in the primal semidefinite program. We also design an algorithm for semidefinite programming with box constraints, achieving a competitive ratio of O(log F*), where F* is a sparsity measure of the semidefinite program. We conclude with an online randomized rounding procedure.
Cite as

Noa Elad, Satyen Kale, and Joseph (Seffi) Naor. Online Semidefinite Programming. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 40:1-40:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{elad_et_al:LIPIcs.ICALP.2016.40,
  author =	{Elad, Noa and Kale, Satyen and Naor, Joseph (Seffi)},
  title =	{{Online Semidefinite Programming}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{40:1--40:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.40},
  URN =		{urn:nbn:de:0030-drops-63205},
  doi =		{10.4230/LIPIcs.ICALP.2016.40},
  annote =	{Keywords: online algorithms, semidefinite programming, primal-dual}
}
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