3 Search Results for "Balkanski, Eric"

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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2024.100

Subquadratic Submodular Maximization with a General Matroid Constraint

Authors: Yusuke Kobayashi and Tatsuya Terao

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

Abstract

We consider fast algorithms for monotone submodular maximization with a general matroid constraint. We present a randomized (1 - 1/e - ε)-approximation algorithm that requires Õ_{ε}(√r n) independence oracle and value oracle queries, where n is the number of elements in the matroid and r ≤ n is the rank of the matroid. This improves upon the previously best algorithm by Buchbinder-Feldman-Schwartz [Mathematics of Operations Research 2017] that requires Õ_{ε}(r² + √rn) queries. Our algorithm is based on continuous relaxation, as with other submodular maximization algorithms in the literature. To achieve subquadratic query complexity, we develop a new rounding algorithm, which is our main technical contribution. The rounding algorithm takes as input a point represented as a convex combination of t bases of a matroid and rounds it to an integral solution. Our rounding algorithm requires Õ(r^{3/2} t) independence oracle queries, while the previously best rounding algorithm by Chekuri-Vondrák-Zenklusen [FOCS 2010] requires O(r² t) independence oracle queries. A key idea in our rounding algorithm is to use a directed cycle of arbitrary length in an auxiliary graph, while the algorithm of Chekuri-Vondrák-Zenklusen focused on directed cycles of length two.

Cite as

Yusuke Kobayashi and Tatsuya Terao. Subquadratic Submodular Maximization with a General Matroid Constraint. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 100:1-100:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kobayashi_et_al:LIPIcs.ICALP.2024.100,
  author =	{Kobayashi, Yusuke and Terao, Tatsuya},
  title =	{{Subquadratic Submodular Maximization with a General Matroid Constraint}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{100:1--100:19},
  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.2024.100},
  URN =		{urn:nbn:de:0030-drops-202437},
  doi =		{10.4230/LIPIcs.ICALP.2024.100},
  annote =	{Keywords: submodular maximization, matroid constraint, approximation algorithm, rounding algorithm, query complexity}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2023.11

Strategyproof Scheduling with Predictions

Authors: Eric Balkanski, Vasilis Gkatzelis, and Xizhi Tan

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract

In their seminal paper that initiated the field of algorithmic mechanism design, Nisan and Ronen [Noam Nisan and Amir Ronen, 1999] studied the problem of designing strategyproof mechanisms for scheduling jobs on unrelated machines aiming to minimize the makespan. They provided a strategyproof mechanism that achieves an n-approximation and they made the bold conjecture that this is the best approximation achievable by any deterministic strategyproof scheduling mechanism. After more than two decades and several efforts, n remains the best known approximation and very recent work by Christodoulou et al. [George Christodoulou et al., 2021] has been able to prove an Ω(√n) approximation lower bound for all deterministic strategyproof mechanisms. This strong negative result, however, heavily depends on the fact that the performance of these mechanisms is evaluated using worst-case analysis. To overcome such overly pessimistic, and often uninformative, worst-case bounds, a surge of recent work has focused on the "learning-augmented framework", whose goal is to leverage machine-learned predictions to obtain improved approximations when these predictions are accurate (consistency), while also achieving near-optimal worst-case approximations even when the predictions are arbitrarily wrong (robustness). In this work, we study the classic strategic scheduling problem of Nisan and Ronen [Noam Nisan and Amir Ronen, 1999] using the learning-augmented framework and give a deterministic polynomial-time strategyproof mechanism that is 6-consistent and 2n-robust. We thus achieve the "best of both worlds": an O(1) consistency and an O(n) robustness that asymptotically matches the best-known approximation. We then extend this result to provide more general worst-case approximation guarantees as a function of the prediction error. Finally, we complement our positive results by showing that any 1-consistent deterministic strategyproof mechanism has unbounded robustness.

Cite as

Eric Balkanski, Vasilis Gkatzelis, and Xizhi Tan. Strategyproof Scheduling with Predictions. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 11:1-11:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{balkanski_et_al:LIPIcs.ITCS.2023.11,
  author =	{Balkanski, Eric and Gkatzelis, Vasilis and Tan, Xizhi},
  title =	{{Strategyproof Scheduling with Predictions}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{11:1--11:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.11},
  URN =		{urn:nbn:de:0030-drops-175143},
  doi =		{10.4230/LIPIcs.ITCS.2023.11},
  annote =	{Keywords: Mechanism Design with Predictions, Strategyproof Scheduling}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2022.113

Budget-Smoothed Analysis for Submodular Maximization

Authors: Aviad Rubinstein and Junyao Zhao

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract

The greedy algorithm for monotone submodular function maximization subject to cardinality constraint is guaranteed to approximate the optimal solution to within a 1-1/e factor. Although it is well known that this guarantee is essentially tight in the worst case - for greedy and in fact any efficient algorithm, experiments show that greedy performs better in practice. We observe that for many applications in practice, the empirical distribution of the budgets (i.e., cardinality constraints) is supported on a wide range, and moreover, all the existing hardness results in theory break under a large perturbation of the budget. To understand the effect of the budget from both algorithmic and hardness perspectives, we introduce a new notion of budget-smoothed analysis. We prove that greedy is optimal for every budget distribution, and we give a characterization for the worst-case submodular functions. Based on these results, we show that on the algorithmic side, under realistic budget distributions, greedy and related algorithms enjoy provably better approximation guarantees, that hold even for worst-case functions, and on the hardness side, there exist hard functions that are fairly robust to all the budget distributions.

Cite as

Aviad Rubinstein and Junyao Zhao. Budget-Smoothed Analysis for Submodular Maximization. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 113:1-113:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{rubinstein_et_al:LIPIcs.ITCS.2022.113,
  author =	{Rubinstein, Aviad and Zhao, Junyao},
  title =	{{Budget-Smoothed Analysis for Submodular Maximization}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{113:1--113:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.113},
  URN =		{urn:nbn:de:0030-drops-157095},
  doi =		{10.4230/LIPIcs.ITCS.2022.113},
  annote =	{Keywords: Submodular optimization, Beyond worst-case analysis, Greedy algorithms, Hardness of approximation}
}

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1 Balkanski, Eric
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1 Kobayashi, Yusuke
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2 Theory of computation → Submodular optimization and polymatroids
1 Theory of computation → Algorithm design techniques
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1 Beyond worst-case analysis
1 Greedy algorithms
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