29 Search Results for "Kleinberg, Robert"

Document
DOI: 10.4230/LIPIcs.ESA.2024.47
Bicriterial Approximation for the Incremental Prize-Collecting Steiner-Tree Problem

Authors: Yann Disser, Svenja M. Griesbach, Max Klimm, and Annette Lutz

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
We consider an incremental variant of the rooted prize-collecting Steiner-tree problem with a growing budget constraint. While no incremental solution exists that simultaneously approximates the optimum for all budgets, we show that a bicriterial (α,μ)-approximation is possible, i.e., a solution that with budget B+α for all B ∈ ℝ_{≥ 0} is a multiplicative μ-approximation compared to the optimum solution with budget B. For the case that the underlying graph is a tree, we present a polynomial-time density-greedy algorithm that computes a (χ,1)-approximation, where χ denotes the eccentricity of the root vertex in the underlying graph, and show that this is best possible. An adaptation of the density-greedy algorithm for general graphs is (γ,2)-competitive where γ is the maximal length of a vertex-disjoint path starting in the root. While this algorithm does not run in polynomial time, it can be adapted to a (γ,3)-competitive algorithm that runs in polynomial time. We further devise a capacity-scaling algorithm that guarantees a (3χ,8)-approximation and, more generally, a ((4𝓁 - 1)χ, (2^{𝓁 + 2})/(2^𝓁 -1))-approximation for every fixed 𝓁 ∈ ℕ.
Cite as

Yann Disser, Svenja M. Griesbach, Max Klimm, and Annette Lutz. Bicriterial Approximation for the Incremental Prize-Collecting Steiner-Tree Problem. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 47:1-47:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{disser_et_al:LIPIcs.ESA.2024.47,
  author =	{Disser, Yann and Griesbach, Svenja M. and Klimm, Max and Lutz, Annette},
  title =	{{Bicriterial Approximation for the Incremental Prize-Collecting Steiner-Tree Problem}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{47:1--47:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.47},
  URN =		{urn:nbn:de:0030-drops-211188},
  doi =		{10.4230/LIPIcs.ESA.2024.47},
  annote =	{Keywords: incremental optimization, competitive analysis, prize-collecting Steiner-tree}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.73
Laminar Matroid Secretary: Greedy Strikes Back

Authors: Zhiyi Huang, Zahra Parsaeian, and Zixuan Zhu

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
We show that a simple greedy algorithm is 4.75-competitive for the Laminar Matroid Secretary Problem, improving the 3√3 ≈ 5.196-competitive algorithm based on the forbidden sets technique (Soto, Turkieltaub, and Verdugo, 2018).
Cite as

Zhiyi Huang, Zahra Parsaeian, and Zixuan Zhu. Laminar Matroid Secretary: Greedy Strikes Back. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 73:1-73:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{huang_et_al:LIPIcs.ESA.2024.73,
  author =	{Huang, Zhiyi and Parsaeian, Zahra and Zhu, Zixuan},
  title =	{{Laminar Matroid Secretary: Greedy Strikes Back}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{73:1--73:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.73},
  URN =		{urn:nbn:de:0030-drops-211443},
  doi =		{10.4230/LIPIcs.ESA.2024.73},
  annote =	{Keywords: Matroid Secretary, Greedy Algorithm, Laminar Matroid}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.105
The Last Success Problem with Samples

Authors: Toru Yoshinaga and Yasushi Kawase

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
The last success problem is an optimal stopping problem that aims to maximize the probability of stopping on the last success in a sequence of independent n Bernoulli trials. In the classical setting where complete information about the distributions is available, Bruss [Bruss, 2000] provided an optimal stopping policy that ensures a winning probability of 1/e. However, assuming complete knowledge of the distributions is unrealistic in many practical applications. This paper investigates a variant of the last success problem where samples from each distribution are available instead of complete knowledge of them. When a single sample from each distribution is allowed, we provide a deterministic policy that guarantees a winning probability of 1/4. This is best possible by the upper bound provided by Nuti and Vondrák [Nuti and Vondr{á}k, 2023]. Furthermore, for any positive constant ε, we show that a constant number of samples from each distribution is sufficient to guarantee a winning probability of 1/e-ε.
Cite as

Toru Yoshinaga and Yasushi Kawase. The Last Success Problem with Samples. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 105:1-105:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{yoshinaga_et_al:LIPIcs.ESA.2024.105,
  author =	{Yoshinaga, Toru and Kawase, Yasushi},
  title =	{{The Last Success Problem with Samples}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{105:1--105:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.105},
  URN =		{urn:nbn:de:0030-drops-211762},
  doi =		{10.4230/LIPIcs.ESA.2024.105},
  annote =	{Keywords: The Last Success Problem, Secretary Problem, Sample Information Model, Optimal Stopping, Online Algorithms}
}
Document
DOI: 10.4230/LIPIcs.AFT.2024.24
Investigating Wrench Attacks: Physical Attacks Targeting Cryptocurrency Users

Authors: Marilyne Ordekian, Gilberto Atondo-Siu, Alice Hutchings, and Marie Vasek

Published in: LIPIcs, Volume 316, 6th Conference on Advances in Financial Technologies (AFT 2024)

Abstract
Cryptocurrency wrench attacks are physical attacks targeting cryptocurrency users in the real world to illegally obtain cryptocurrencies. These attacks significantly undermine the efficacy of existing digital security norms when confronted with real-world threats. We present the first comprehensive study on wrench attacks. We propose a theoretical approach to defining wrench attacks per criminal law norms, and an interdisciplinary empirical approach to measure their incidence. Leveraging three data sources, we perform crime script analysis, detecting incidents globally across 10 interviews with victims and experts, 146 news articles, and 37 online forums. Our findings reveal diverse groups of attackers ranging from organized crime groups to friends and family, various modi operandi, and different forms of attacks varying from blackmail to murder. Despite existing since Bitcoin’s early days, these attacks are underreported due to revictimization fears. Additionally, unlike other cryptocurrency crimes, users with advanced security experience were not immune to them. We identify potential vulnerabilities in users' behavior and encourage cryptocurrency holders to lean into digital as well as physical safety measures to protect themselves and their cryptocurrency. We offer actionable recommendations for the security community and regulators, highlighting the double-edged sword of Know Your Customer policies.
Cite as

Marilyne Ordekian, Gilberto Atondo-Siu, Alice Hutchings, and Marie Vasek. Investigating Wrench Attacks: Physical Attacks Targeting Cryptocurrency Users. In 6th Conference on Advances in Financial Technologies (AFT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 316, pp. 24:1-24:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ordekian_et_al:LIPIcs.AFT.2024.24,
  author =	{Ordekian, Marilyne and Atondo-Siu, Gilberto and Hutchings, Alice and Vasek, Marie},
  title =	{{Investigating Wrench Attacks: Physical Attacks Targeting Cryptocurrency Users}},
  booktitle =	{6th Conference on Advances in Financial Technologies (AFT 2024)},
  pages =	{24:1--24:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-345-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{316},
  editor =	{B\"{o}hme, Rainer and Kiffer, Lucianna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2024.24},
  URN =		{urn:nbn:de:0030-drops-209609},
  doi =		{10.4230/LIPIcs.AFT.2024.24},
  annote =	{Keywords: cryptocurrency, Bitcoin, crime, wrench attack, physical attack}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.9
On the Generalized Mean Densest Subgraph Problem: Complexity and Algorithms

Authors: Karthekeyan Chandrasekaran, Chandra Chekuri, Manuel R. Torres, and Weihao Zhu

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
Dense subgraph discovery is an important problem in graph mining and network analysis with several applications. Two canonical polynomial-time solvable problems here are to find a maxcore (subgraph of maximum min degree) and to find a densest subgraph (subgraph of maximum average degree). Both of these problems can be solved in polynomial time. Veldt, Benson, and Kleinberg [Veldt et al., 2021] introduced the generalized p-mean densest subgraph problem which captures the maxcore problem when p = -∞ and the densest subgraph problem when p = 1. They observed that for p ≥ 1, the objective function is supermodular and hence the problem can be solved in polynomial time. In this work, we focus on the p-mean densest subgraph problem for p ∈ (-∞, 1). We prove that for every p ∈ (-∞,1), the problem is NP-hard, thus resolving an open question from [Veldt et al., 2021]. We also show that for every p ∈ (0,1), the weighted version of the problem is APX-hard. On the algorithmic front, we describe two simple 1/2-approximation algorithms for every p ∈ (-∞, 1). We complement the approximation algorithms by exhibiting non-trivial instances on which the algorithms simultaneously achieve an approximation factor of at most 1/2.
Cite as

Karthekeyan Chandrasekaran, Chandra Chekuri, Manuel R. Torres, and Weihao Zhu. On the Generalized Mean Densest Subgraph Problem: Complexity and Algorithms. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chandrasekaran_et_al:LIPIcs.APPROX/RANDOM.2024.9,
  author =	{Chandrasekaran, Karthekeyan and Chekuri, Chandra and Torres, Manuel R. and Zhu, Weihao},
  title =	{{On the Generalized Mean Densest Subgraph Problem: Complexity and Algorithms}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{9:1--9:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.9},
  URN =		{urn:nbn:de:0030-drops-210025},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.9},
  annote =	{Keywords: Densest subgraph problem, Hardness of approximation, Approximation algorithms}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.12
Universal Optimization for Non-Clairvoyant Subadditive Joint Replenishment

Authors: Tomer Ezra, Stefano Leonardi, Michał Pawłowski, Matteo Russo, and Seeun William Umboh

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
The online joint replenishment problem (JRP) is a fundamental problem in the area of online problems with delay. Over the last decade, several works have studied generalizations of JRP with different cost functions for servicing requests. Most prior works on JRP and its generalizations have focused on the clairvoyant setting. Recently, Touitou [Noam Touitou, 2023] developed a non-clairvoyant framework that provided an O(√{n log n}) upper bound for a wide class of generalized JRP, where n is the number of request types. We advance the study of non-clairvoyant algorithms by providing a simpler, modular framework that matches the competitive ratio established by Touitou for the same class of generalized JRP. Our key insight is to leverage universal algorithms for Set Cover to approximate arbitrary monotone subadditive functions using a simple class of functions termed disjoint. This allows us to reduce the problem to several independent instances of the TCP Acknowledgement problem, for which a simple 2-competitive non-clairvoyant algorithm is known. The modularity of our framework is a major advantage as it allows us to tailor the reduction to specific problems and obtain better competitive ratios. In particular, we obtain tight O(√n)-competitive algorithms for two significant problems: Multi-Level Aggregation and Weighted Symmetric Subadditive Joint Replenishment. We also show that, in contrast, Touitou’s algorithm is Ω(√{n log n})-competitive for both of these problems.
Cite as

Tomer Ezra, Stefano Leonardi, Michał Pawłowski, Matteo Russo, and Seeun William Umboh. Universal Optimization for Non-Clairvoyant Subadditive Joint Replenishment. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 12:1-12:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ezra_et_al:LIPIcs.APPROX/RANDOM.2024.12,
  author =	{Ezra, Tomer and Leonardi, Stefano and Paw{\l}owski, Micha{\l} and Russo, Matteo and Umboh, Seeun William},
  title =	{{Universal Optimization for Non-Clairvoyant Subadditive Joint Replenishment}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{12:1--12:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.12},
  URN =		{urn:nbn:de:0030-drops-210050},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.12},
  annote =	{Keywords: Set Cover, Joint Replenishment, TCP-Acknowledgment, Subadditive Function Approximation, Multi-Level Aggregation}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.13
The Average-Value Allocation Problem

Authors: Kshipra Bhawalkar, Zhe Feng, Anupam Gupta, Aranyak Mehta, David Wajc, and Di Wang

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
We initiate the study of centralized algorithms for welfare-maximizing allocation of goods to buyers subject to average-value constraints. We show that this problem is NP-hard to approximate beyond a factor of e/(e-1), and provide a 4e/(e-1)-approximate offline algorithm. For the online setting, we show that no non-trivial approximations are achievable under adversarial arrivals. Under i.i.d. arrivals, we present a polytime online algorithm that provides a constant approximation of the optimal (computationally-unbounded) online algorithm. In contrast, we show that no constant approximation of the ex-post optimum is achievable by an online algorithm.
Cite as

Kshipra Bhawalkar, Zhe Feng, Anupam Gupta, Aranyak Mehta, David Wajc, and Di Wang. The Average-Value Allocation Problem. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 13:1-13:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bhawalkar_et_al:LIPIcs.APPROX/RANDOM.2024.13,
  author =	{Bhawalkar, Kshipra and Feng, Zhe and Gupta, Anupam and Mehta, Aranyak and Wajc, David and Wang, Di},
  title =	{{The Average-Value Allocation Problem}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{13:1--13:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.13},
  URN =		{urn:nbn:de:0030-drops-210062},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.13},
  annote =	{Keywords: Resource allocation, return-on-spend constraint, approximation algorithm, online algorithm}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.23
On Instance-Optimal Algorithms for a Generalization of Nuts and Bolts and Generalized Sorting

Authors: Mayank Goswami and Riko Jacob

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
We generalize the classical nuts and bolts problem to a setting where the input is a collection of n nuts and m bolts, and there is no promise of any matching pairs. It is not allowed to compare a nut directly with a nut or a bolt directly with a bolt, and the goal is to perform the fewest nut-bolt comparisons to discover the partial order between the nuts and bolts. We term this problem bipartite sorting. We show that instances of bipartite sorting of the same size exhibit a wide range of complexity, and propose to perform a fine-grained analysis for this problem. We rule out straightforward notions of instance-optimality as being too stringent, and adopt a neighborhood-based definition. Our definition may be of independent interest as a unifying lens for instance-optimal algorithms for other static problems existing in literature. This includes problems like sorting (Estivill-Castro and Woods, ACM Comput. Surv. 1992), convex hull (Afshani, Barbay and Chan, JACM 2017), adaptive joins (Demaine, López-Ortiz and Munro, SODA 2000), and the recent concept of universal optimality for graphs (Haeupler, Hladík, Rozhoň, Tarjan and Tětek, 2023). As our main result on bipartite sorting, we give a randomized algorithm that is within a factor of O(log³(n+m)) of being instance-optimal w.h.p., with respect to the neighborhood-based definition. As our second contribution, we generalize bipartite sorting to DAG sorting, when the underlying DAG is not necessarily bipartite. As an unexpected consequence of a simple algorithm for DAG sorting, we rule out a potential lower bound on the widely-studied problem of sorting with priced information, posed by (Charikar, Fagin, Guruswami, Kleinberg, Raghavan and Sahai, STOC 2000). In this problem, comparing keys i and j has a known cost c_{ij} ∈ ℝ^+ ∪ {∞}, and the goal is to sort the keys in an instance-optimal way, by keeping the total cost of an algorithm as close as possible to ∑_{i=1}^{n-1} c_{x(i)x(i+1)}. Here x(1) < ⋯ < x(n) is the sorted order. While several special cases of cost functions have received a lot of attention in the community, no progress on the general version with arbitrary costs has been reported so far. One reason for this lack of progress seems to be a widely-cited Ω(n) lower bound on the competitive ratio for finding the maximum. This Ω(n) lower bound by (Gupta and Kumar, FOCS 2000) uses costs in {0,1,n, ∞}, and although not extended to sorting, this barrier seems to have stalled any progress on the general cost case. We rule out such a potential lower bound by showing the existence of an algorithm with a Õ(n^{3/4}) competitive ratio for the {0,1,n,∞} cost version. This generalizes the setting of generalized sorting proposed by (Huang, Kannan and Khanna, FOCS 2011), where the costs are either 1 or infinity, and the cost of the cheapest proof is always n-1.
Cite as

Mayank Goswami and Riko Jacob. On Instance-Optimal Algorithms for a Generalization of Nuts and Bolts and Generalized Sorting. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 23:1-23:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{goswami_et_al:LIPIcs.APPROX/RANDOM.2024.23,
  author =	{Goswami, Mayank and Jacob, Riko},
  title =	{{On Instance-Optimal Algorithms for a Generalization of Nuts and Bolts and Generalized Sorting}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{23:1--23:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.23},
  URN =		{urn:nbn:de:0030-drops-210168},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.23},
  annote =	{Keywords: Sorting, Priced Information, Instance Optimality, Nuts and Bolts}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.42
Matrix Multiplication Verification Using Coding Theory

Authors: Huck Bennett, Karthik Gajulapalli, Alexander Golovnev, and Evelyn Warton

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
We study the Matrix Multiplication Verification Problem (MMV) where the goal is, given three n × n matrices A, B, and C as input, to decide whether AB = C. A classic randomized algorithm by Freivalds (MFCS, 1979) solves MMV in Õ(n²) time, and a longstanding challenge is to (partially) derandomize it while still running in faster than matrix multiplication time (i.e., in o(n^ω) time). To that end, we give two algorithms for MMV in the case where AB - C is sparse. Specifically, when AB - C has at most O(n^δ) non-zero entries for a constant 0 ≤ δ < 2, we give (1) a deterministic O(n^(ω-ε))-time algorithm for constant ε = ε(δ) > 0, and (2) a randomized Õ(n²)-time algorithm using δ/2 ⋅ log₂ n + O(1) random bits. The former algorithm is faster than the deterministic algorithm of Künnemann (ESA, 2018) when δ ≥ 1.056, and the latter algorithm uses fewer random bits than the algorithm of Kimbrel and Sinha (IPL, 1993), which runs in the same time and uses log₂ n + O(1) random bits (in turn fewer than Freivalds’s algorithm). Our algorithms are simple and use techniques from coding theory. Let H be a parity-check matrix of a Maximum Distance Separable (MDS) code, and let G = (I | G') be a generator matrix of a (possibly different) MDS code in systematic form. Our deterministic algorithm uses fast rectangular matrix multiplication to check whether HAB = HC and H(AB)^T = H(C^T), and our randomized algorithm samples a uniformly random row g' from G' and checks whether g'AB = g'C and g'(AB)^T = g'C^T. We additionally study the complexity of MMV. We first show that all algorithms in a natural class of deterministic linear algebraic algorithms for MMV (including ours) require Ω(n^ω) time. We also show a barrier to proving a super-quadratic running time lower bound for matrix multiplication (and hence MMV) under the Strong Exponential Time Hypothesis (SETH). Finally, we study relationships between natural variants and special cases of MMV (with respect to deterministic Õ(n²)-time reductions).
Cite as

Huck Bennett, Karthik Gajulapalli, Alexander Golovnev, and Evelyn Warton. Matrix Multiplication Verification Using Coding Theory. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 42:1-42:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bennett_et_al:LIPIcs.APPROX/RANDOM.2024.42,
  author =	{Bennett, Huck and Gajulapalli, Karthik and Golovnev, Alexander and Warton, Evelyn},
  title =	{{Matrix Multiplication Verification Using Coding Theory}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{42:1--42:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.42},
  URN =		{urn:nbn:de:0030-drops-210352},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.42},
  annote =	{Keywords: Matrix Multiplication Verification, Derandomization, Sparse Matrices, Error-Correcting Codes, Hardness Barriers, Reductions}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.25
Multiway Cuts with a Choice of Representatives

Authors: Kristóf Bérczi, Tamás Király, and Daniel P. Szabo

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
In the Multiway Cut problem, we are given an undirected graph with nonnegative edge weights and a subset of k terminals, and the goal is to determine a set of edges of minimum total weight whose removal disconnects each terminal from the rest. The problem is APX-hard for k ≥ 3, and an extensive line of research has concentrated on closing the gap between the best upper and lower bounds for approximability and inapproximability, respectively. In this paper, we study several generalizations of Multiway Cut where the terminals can be chosen as representatives from sets of candidates T₁,…,T_q. In this setting, one is allowed to choose these representatives so that the minimum-weight cut separating these sets via their representatives is as small as possible. We distinguish different cases depending on (A) whether the representative of a candidate set has to be separated from the other candidate sets completely or only from the representatives, and (B) whether there is a single representative for each candidate set or the choice of representative is independent for each pair of candidate sets. For fixed q, we give approximation algorithms for each of these problems that match the best known approximation guarantee for Multiway Cut. Our technical contribution is a new extension of the CKR relaxation that preserves approximation guarantees. For general q, we show o(log q)-inapproximability for all cases where the choice of representatives may depend on the pair of candidate sets, as well as for the case where the goal is to separate a fixed node from a single representative from each candidate set. As a positive result, we give a 2-approximation algorithm for the case where we need to choose a single representative from each candidate set. This is a generalization of the (2-2/k)-approximation for k-Cut, and we can solve it by relating the tree case to optimization over a gammoid.
Cite as

Kristóf Bérczi, Tamás Király, and Daniel P. Szabo. Multiway Cuts with a Choice of Representatives. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{berczi_et_al:LIPIcs.MFCS.2024.25,
  author =	{B\'{e}rczi, Krist\'{o}f and Kir\'{a}ly, Tam\'{a}s and Szabo, Daniel P.},
  title =	{{Multiway Cuts with a Choice of Representatives}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{25:1--25:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.25},
  URN =		{urn:nbn:de:0030-drops-205813},
  doi =		{10.4230/LIPIcs.MFCS.2024.25},
  annote =	{Keywords: Approximation algorithms, Multiway cut, CKR relaxation, Steiner multicut}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.36
Distance to Transitivity: New Parameters for Taming Reachability in Temporal Graphs

Authors: Arnaud Casteigts, Nils Morawietz, and Petra Wolf

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
A temporal graph is a graph whose edges only appear at certain points in time. Reachability in these graphs is defined in terms of paths that traverse the edges in chronological order (temporal paths). This form of reachability is neither symmetric nor transitive, the latter having important consequences on the computational complexity of even basic questions, such as computing temporal connected components. In this paper, we introduce several parameters that capture how far a temporal graph 𝒢 is from being transitive, namely, vertex-deletion distance to transitivity and arc-modification distance to transitivity, both being applied to the reachability graph of 𝒢. We illustrate the impact of these parameters on the temporal connected component problem, obtaining several tractability results in terms of fixed-parameter tractability and polynomial kernels. Significantly, these results are obtained without restrictions of the underlying graph, the snapshots, or the lifetime of the input graph. As such, our results isolate the impact of non-transitivity and confirm the key role that it plays in the hardness of temporal graph problems.
Cite as

Arnaud Casteigts, Nils Morawietz, and Petra Wolf. Distance to Transitivity: New Parameters for Taming Reachability in Temporal Graphs. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 36:1-36:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{casteigts_et_al:LIPIcs.MFCS.2024.36,
  author =	{Casteigts, Arnaud and Morawietz, Nils and Wolf, Petra},
  title =	{{Distance to Transitivity: New Parameters for Taming Reachability in Temporal Graphs}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{36:1--36:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.36},
  URN =		{urn:nbn:de:0030-drops-205923},
  doi =		{10.4230/LIPIcs.MFCS.2024.36},
  annote =	{Keywords: Temporal graphs, Parameterized complexity, Reachability, Transitivity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.38
Algorithms and Complexity for Path Covers of Temporal DAGs

Authors: Dibyayan Chakraborty, Antoine Dailly, Florent Foucaud, and Ralf Klasing

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
A path cover of a digraph is a collection of paths collectively containing its vertex set. A path cover with minimum cardinality for a directed acyclic graph can be found in polynomial time [Fulkerson, AMS'56; Cáceres et al., SODA'22]. Moreover, Dilworth’s celebrated theorem on chain coverings of partially ordered sets equivalently states that the minimum size of a path cover of a DAG is equal to the maximum size of a set of mutually unreachable vertices. In this paper, we examine how far these classic results can be extended to a dynamic setting. A temporal digraph has an arc set that changes over discrete time-steps; if the underlying digraph is acyclic, then it is a temporal DAG. A temporal path is a directed path in the underlying digraph, such that the time-steps of arcs are strictly increasing along the path. Two temporal paths are temporally disjoint if they do not occupy any vertex at the same time. A temporal path cover is a collection 𝒞 of temporal paths that covers all vertices, and 𝒞 is temporally disjoint if all its temporal paths are pairwise temporally disjoint. We study the computational complexities of the problems of finding a minimum-size temporal (disjoint) path cover (denoted as Temporal Path Cover and Temporally Disjoint Path Cover). On the negative side, we show that both Temporal Path Cover and Temporally Disjoint Path Cover are NP-hard even when the underlying DAG is planar, bipartite, subcubic, and there are only two arc-disjoint time-steps. Moreover, Temporally Disjoint Path Cover remains NP-hard even on temporal oriented trees. We also observe that natural temporal analogues of Dilworth’s theorem on these classes of temporal DAGs do not hold. In contrast, we show that Temporal Path Cover is polynomial-time solvable on temporal oriented trees by a reduction to Clique Cover for (static undirected) weakly chordal graphs (a subclass of perfect graphs for which Clique Cover admits an efficient algorithm). This highlights an interesting algorithmic difference between the two problems. Although it is NP-hard on temporal oriented trees, Temporally Disjoint Path Cover becomes polynomial-time solvable on temporal oriented lines and temporal rooted directed trees. Motivated by the hardness result on trees, we show that, in contrast, Temporal Path Cover admits an XP time algorithm with respect to parameter t_max + tw, where t_max is the maximum time-step and tw is the treewidth of the underlying static undirected graph; moreover, Temporally Disjoint Path Cover admits an FPT algorithm with respect to the same parameterization.
Cite as

Dibyayan Chakraborty, Antoine Dailly, Florent Foucaud, and Ralf Klasing. Algorithms and Complexity for Path Covers of Temporal DAGs. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 38:1-38:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chakraborty_et_al:LIPIcs.MFCS.2024.38,
  author =	{Chakraborty, Dibyayan and Dailly, Antoine and Foucaud, Florent and Klasing, Ralf},
  title =	{{Algorithms and Complexity for Path Covers of Temporal DAGs}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{38:1--38:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.38},
  URN =		{urn:nbn:de:0030-drops-205940},
  doi =		{10.4230/LIPIcs.MFCS.2024.38},
  annote =	{Keywords: Temporal Graphs, Dilworth’s Theorem, DAGs, Path Cover, Temporally Disjoint Paths, Algorithms, Oriented Trees, Treewidth}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.6
The Entangled Quantum Polynomial Hierarchy Collapses

Authors: Sabee Grewal and Justin Yirka

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract
We introduce the entangled quantum polynomial hierarchy, QEPH, as the class of problems that are efficiently verifiable given alternating quantum proofs that may be entangled with each other. We prove QEPH collapses to its second level. In fact, we show that a polynomial number of alternations collapses to just two. As a consequence, QEPH = QRG(1), the class of problems having one-turn quantum refereed games, which is known to be contained in PSPACE. This is in contrast to the unentangled quantum polynomial hierarchy, QPH, which contains QMA(2). We also introduce DistributionQCPH, a generalization of the quantum-classical polynomial hierarchy QCPH where the provers send probability distributions over strings (instead of strings). We prove DistributionQCPH = QCPH, suggesting that only quantum superposition (not classical probability) increases the computational power of these hierarchies. To prove this equality, we generalize a game-theoretic result of Lipton and Young (1994) which says that, without loss of generality, the provers can send uniform distributions over a polynomial-size support. We also prove the analogous result for the polynomial hierarchy, i.e., DistributionPH = PH. Finally, we show that PH and QCPH are contained in QPH, resolving an open question of Gharibian et al. (2022).
Cite as

Sabee Grewal and Justin Yirka. The Entangled Quantum Polynomial Hierarchy Collapses. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 6:1-6:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{grewal_et_al:LIPIcs.CCC.2024.6,
  author =	{Grewal, Sabee and Yirka, Justin},
  title =	{{The Entangled Quantum Polynomial Hierarchy Collapses}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{6:1--6:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.6},
  URN =		{urn:nbn:de:0030-drops-204028},
  doi =		{10.4230/LIPIcs.CCC.2024.6},
  annote =	{Keywords: Polynomial hierarchy, Entangled proofs, Correlated proofs, Minimax}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.8
Practical Computation of Graph VC-Dimension

Authors: David Coudert, Mónika Csikós, Guillaume Ducoffe, and Laurent Viennot

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
For any set system ℋ = (V,ℛ), ℛ ⊆ 2^V, a subset S ⊆ V is called shattered if every S' ⊆ S results from the intersection of S with some set in ℛ. The VC-dimension of ℋ is the size of a largest shattered set in V. In this paper, we focus on the problem of computing the VC-dimension of graphs. In particular, given a graph G = (V,E), the VC-dimension of G is defined as the VC-dimension of (V, N), where N contains each subset of V that can be obtained as the closed neighborhood of some vertex v ∈ V in G. Our main contribution is an algorithm for computing the VC-dimension of any graph, whose effectiveness is shown through experiments on various types of practical graphs, including graphs with millions of vertices. A key aspect of its efficiency resides in the fact that practical graphs have small VC-dimension, up to 8 in our experiments. As a side-product, we present several new bounds relating the graph VC-dimension to other classical graph theoretical notions. We also establish the W[1]-hardness of the graph VC-dimension problem by extending a previous result for arbitrary set systems.
Cite as

David Coudert, Mónika Csikós, Guillaume Ducoffe, and Laurent Viennot. Practical Computation of Graph VC-Dimension. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{coudert_et_al:LIPIcs.SEA.2024.8,
  author =	{Coudert, David and Csik\'{o}s, M\'{o}nika and Ducoffe, Guillaume and Viennot, Laurent},
  title =	{{Practical Computation of Graph VC-Dimension}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{8:1--8:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.8},
  URN =		{urn:nbn:de:0030-drops-203731},
  doi =		{10.4230/LIPIcs.SEA.2024.8},
  annote =	{Keywords: VC-dimension, graph, algorithm}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2024.2
Abstraction-Based Decision Making for Statistical Properties (Invited Talk)

Authors: Filip Cano, Thomas A. Henzinger, Bettina Könighofer, Konstantin Kueffner, and Kaushik Mallik

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract
Sequential decision-making in probabilistic environments is a fundamental problem with many applications in AI and economics. In this paper, we present an algorithm for synthesizing sequential decision-making agents that optimize statistical properties such as maximum and average response times. In the general setting of sequential decision-making, the environment is modeled as a random process that generates inputs. The agent responds to each input, aiming to maximize rewards and minimize costs within a specified time horizon. The corresponding synthesis problem is known to be PSPACE-hard. We consider the special case where the input distribution, reward, and cost depend on input-output statistics specified by counter automata. For such problems, this paper presents the first PTIME synthesis algorithms. We introduce the notion of statistical abstraction, which clusters statistically indistinguishable input-output sequences into equivalence classes. This abstraction allows for a dynamic programming algorithm whose complexity grows polynomially with the considered horizon, making the statistical case exponentially more efficient than the general case. We evaluate our algorithm on three different application scenarios of a client-server protocol, where multiple clients compete via bidding to gain access to the service offered by the server. The synthesized policies optimize profit while guaranteeing that none of the server’s clients is disproportionately starved of the service.
Cite as

Filip Cano, Thomas A. Henzinger, Bettina Könighofer, Konstantin Kueffner, and Kaushik Mallik. Abstraction-Based Decision Making for Statistical Properties (Invited Talk). In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 2:1-2:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{cano_et_al:LIPIcs.FSCD.2024.2,
  author =	{Cano, Filip and Henzinger, Thomas A. and K\"{o}nighofer, Bettina and Kueffner, Konstantin and Mallik, Kaushik},
  title =	{{Abstraction-Based Decision Making for Statistical Properties}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{2:1--2:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.2},
  URN =		{urn:nbn:de:0030-drops-203310},
  doi =		{10.4230/LIPIcs.FSCD.2024.2},
  annote =	{Keywords: Abstract interpretation, Sequential decision making, Counter machines}
}
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