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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2026.17

Competitive Bundle Trading

Authors: Yossi Azar, Niv Buchbinder, Roie Levin, and Or Vardi

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract

Allocating a set of resources to an online sequence of customers is a fundamental problem in online algorithms with an extensive history. However, the natural extension where the algorithm is also allowed to purchase inventory from suppliers, who also arrive online, is essentially unexplored. We study this general trading problem under the objective of profit maximization, which is the difference between revenue from sales and cost of purchases. Maximizing the difference between two competing quantities is significantly more challenging than the sell-only case. We show a logarithmic competitive ratio relative to the optimal offline solution. Our algorithm is an exponential-weight–update dynamic pricing scheme, and our analysis dual-fits the algorithm’s profit with respect to a linear programming relaxation that upper bounds the optimal offline profit; we also prove (nearly) matching lower bounds. Finally, we extend our results by designing an incentive-compatible mechanism for the setting in which customers are strategic and may misreport their true valuations.

Cite as

Yossi Azar, Niv Buchbinder, Roie Levin, and Or Vardi. Competitive Bundle Trading. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 17:1-17:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{azar_et_al:LIPIcs.ICALP.2026.17,
  author =	{Azar, Yossi and Buchbinder, Niv and Levin, Roie and Vardi, Or},
  title =	{{Competitive Bundle Trading}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{17:1--17:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael 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.2026.17},
  URN =		{urn:nbn:de:0030-drops-264066},
  doi =		{10.4230/LIPIcs.ICALP.2026.17},
  annote =	{Keywords: Online algorithms, competitive analysis, algorithmic game theory, mechanism design, dynamic pricing, resource allocation}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2020.84

Finding Skewed Subcubes Under a Distribution

Authors: Parikshit Gopalan, Roie Levin, and Udi Wieder

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract

Say that we are given samples from a distribution ψ over an n-dimensional space. We expect or desire ψ to behave like a product distribution (or a k-wise independent distribution over its marginals for small k). We propose the problem of enumerating/list-decoding all large subcubes where the distribution ψ deviates markedly from what we expect; we refer to such subcubes as skewed subcubes. Skewed subcubes are certificates of dependencies between small subsets of variables in ψ. We motivate this problem by showing that it arises naturally in the context of algorithmic fairness and anomaly detection. In this work we focus on the special but important case where the space is the Boolean hypercube, and the expected marginals are uniform. We show that the obvious definition of skewed subcubes can lead to intractable list sizes, and propose a better definition of a minimal skewed subcube, which are subcubes whose skew cannot be attributed to a larger subcube that contains it. Our main technical contribution is a list-size bound for this definition and an algorithm to efficiently find all such subcubes. Both the bound and the algorithm rely on Fourier-analytic techniques, especially the powerful hypercontractive inequality. On the lower bounds side, we show that finding skewed subcubes is as hard as the sparse noisy parity problem, and hence our algorithms cannot be improved on substantially without a breakthrough on this problem which is believed to be intractable. Motivated by this, we study alternate models allowing query access to ψ where finding skewed subcubes might be easier.

Cite as

Parikshit Gopalan, Roie Levin, and Udi Wieder. Finding Skewed Subcubes Under a Distribution. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 84:1-84:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{gopalan_et_al:LIPIcs.ITCS.2020.84,
  author =	{Gopalan, Parikshit and Levin, Roie and Wieder, Udi},
  title =	{{Finding Skewed Subcubes Under a Distribution}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{84:1--84:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.84},
  URN =		{urn:nbn:de:0030-drops-117691},
  doi =		{10.4230/LIPIcs.ITCS.2020.84},
  annote =	{Keywords: Fourier Analysis, Anomaly Detection, Algorithmic Fairness, Probability, Unsupervised Learning}
}

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Documents authored by Levin, Roie

Competitive Bundle Trading

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Finding Skewed Subcubes Under a Distribution

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