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Documents authored by Buchbinder, Niv

Document
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.2021.21
Metrical Service Systems with Transformations

Authors: Sébastien Bubeck, Niv Buchbinder, Christian Coester, and Mark Sellke

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract
We consider a generalization of the fundamental online metrical service systems (MSS) problem where the feasible region can be transformed between requests. In this problem, which we call T-MSS, an algorithm maintains a point in a metric space and has to serve a sequence of requests. Each request is a map (transformation) f_t: A_t → B_t between subsets A_t and B_t of the metric space. To serve it, the algorithm has to go to a point a_t ∈ A_t, paying the distance from its previous position. Then, the transformation is applied, modifying the algorithm’s state to f_t(a_t). Such transformations can model, e.g., changes to the environment that are outside of an algorithm’s control, and we therefore do not charge any additional cost to the algorithm when the transformation is applied. The transformations also allow to model requests occurring in the k-taxi problem. We show that for α-Lipschitz transformations, the competitive ratio is Θ(α)^{n-2} on n-point metrics. Here, the upper bound is achieved by a deterministic algorithm and the lower bound holds even for randomized algorithms. For the k-taxi problem, we prove a competitive ratio of Õ((nlog k)²). For chasing convex bodies, we show that even with contracting transformations no competitive algorithm exists. The problem T-MSS has a striking connection to the following deep mathematical question: Given a finite metric space M, what is the required cardinality of an extension M̂ ⊇ M where each partial isometry on M extends to an automorphism? We give partial answers for special cases.
Cite as

Sébastien Bubeck, Niv Buchbinder, Christian Coester, and Mark Sellke. Metrical Service Systems with Transformations. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 21:1-21:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bubeck_et_al:LIPIcs.ITCS.2021.21,
  author =	{Bubeck, S\'{e}bastien and Buchbinder, Niv and Coester, Christian and Sellke, Mark},
  title =	{{Metrical Service Systems with Transformations}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{21:1--21:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.21},
  URN =		{urn:nbn:de:0030-drops-135608},
  doi =		{10.4230/LIPIcs.ITCS.2021.21},
  annote =	{Keywords: Online algorithms, competitive analysis, metrical task systems, k-taxi}
}
Document
DOI: 10.4230/LIPIcs.ESA.2017.22
Online Algorithms for Maximum Cardinality Matching with Edge Arrivals

Authors: Niv Buchbinder, Danny Segev, and Yevgeny Tkach

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
In the adversarial edge arrival model for maximum cardinality matching, edges of an unknown graph are revealed one-by-one in arbitrary order, and should be irrevocably accepted or rejected. Here, the goal of an online algorithm is to maximize the number of accepted edges while maintaining a feasible matching at any point in time. For this model, the standard greedy heuristic is 1/2-competitive, and on the other hand, no algorithm that outperforms this ratio is currently known, even for very simple graphs. We present a clean Min-Index framework for devising a family of randomized algorithms, and provide a number of positive and negative results in this context. Among these results, we present a 5/9-competitive algorithm when the underlying graph is a forest, and prove that this ratio is best possible within the Min-Index framework. In addition, we prove a new general upper bound of 2/(3+1/phi^2) ~ 0.5914 on the competitiveness of any algorithm in the edge arrival model. Interestingly, this bound holds even for an easier model in which vertices (along with their adjacent edges) arrive online, and when the underlying graph is a tree of maximum degree at most 3.
Cite as

Niv Buchbinder, Danny Segev, and Yevgeny Tkach. Online Algorithms for Maximum Cardinality Matching with Edge Arrivals. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 22:1-22:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{buchbinder_et_al:LIPIcs.ESA.2017.22,
  author =	{Buchbinder, Niv and Segev, Danny and Tkach, Yevgeny},
  title =	{{Online Algorithms for Maximum Cardinality Matching with Edge Arrivals}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{22:1--22:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.22},
  URN =		{urn:nbn:de:0030-drops-78206},
  doi =		{10.4230/LIPIcs.ESA.2017.22},
  annote =	{Keywords: Maximum matching, online algorithms, competitive analysis, primal-dual method}
}
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