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Documents authored by Schvartzman, Ariel

Document
Approximately Strategyproof Tournament Rules: On Large Manipulating Sets and Cover-Consistence

Authors: Ariel Schvartzman, S. Matthew Weinberg, Eitan Zlatin, and Albert Zuo

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

Abstract
We consider the manipulability of tournament rules, in which n teams play a round robin tournament and a winner is (possibly randomly) selected based on the outcome of all binom{n}{2} matches. Prior work defines a tournament rule to be k-SNM-α if no set of ≤ k teams can fix the ≤ binom{k}{2} matches among them to increase their probability of winning by >α and asks: for each k, what is the minimum α(k) such that a Condorcet-consistent (i.e. always selects a Condorcet winner when one exists) k-SNM-α(k) tournament rule exists? A simple example witnesses that α(k) ≥ (k-1)/(2k-1) for all k, and [Jon Schneider et al., 2017] conjectures that this is tight (and prove it is tight for k=2). Our first result refutes this conjecture: there exists a sufficiently large k such that no Condorcet-consistent tournament rule is k-SNM-1/2. Our second result leverages similar machinery to design a new tournament rule which is k-SNM-2/3 for all k (and this is the first tournament rule which is k-SNM-(<1) for all k). Our final result extends prior work, which proves that single-elimination bracket with random seeding is 2-SNM-1/3 [Jon Schneider et al., 2017], in a different direction by seeking a stronger notion of fairness than Condorcet-consistence. We design a new tournament rule, which we call Randomized-King-of-the-Hill, which is 2-SNM-1/3 and cover-consistent (the winner is an uncovered team with probability 1).

Cite as

Ariel Schvartzman, S. Matthew Weinberg, Eitan Zlatin, and Albert Zuo. Approximately Strategyproof Tournament Rules: On Large Manipulating Sets and Cover-Consistence. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 3:1-3:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

```@InProceedings{schvartzman_et_al:LIPIcs.ITCS.2020.3,
author =	{Schvartzman, Ariel and Weinberg, S. Matthew and Zlatin, Eitan and Zuo, Albert},
title =	{{Approximately Strategyproof Tournament Rules: On Large Manipulating Sets and Cover-Consistence}},
booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
pages =	{3:1--3:25},
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},
URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.3},
URN =		{urn:nbn:de:0030-drops-116881},
doi =		{10.4230/LIPIcs.ITCS.2020.3},
annote =	{Keywords: Tournament design, Non-manipulability, Cover-consistence, Strategyproofness}
}```
Document
Coding in Undirected Graphs Is Either Very Helpful or Not Helpful at All

Authors: Mark Braverman, Sumegha Garg, and Ariel Schvartzman

Published in: LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)

Abstract
While it is known that using network coding can significantly improve the throughput of directed networks, it is a notorious open problem whether coding yields any advantage over the multicommodity flow (MCF) rate in undirected networks. It was conjectured that the answer is no. In this paper we show that even a small advantage over MCF can be amplified to yield a near-maximum possible gap. We prove that any undirected network with k source-sink pairs that exhibits a (1+epsilon) gap between its MCF rate and its network coding rate can be used to construct a family of graphs G' whose gap is log(|G'|)^c for some constant c < 1. The resulting gap is close to the best currently known upper bound, log(|G'|), which follows from the connection between MCF and sparsest cuts. Our construction relies on a gap-amplifying graph tensor product that, given two graphs G1,G2 with small gaps, creates another graph G with a gap that is equal to the product of the previous two, at the cost of increasing the size of the graph. We iterate this process to obtain a gap of log(|G'|)^c from any initial gap.

Cite as

Mark Braverman, Sumegha Garg, and Ariel Schvartzman. Coding in Undirected Graphs Is Either Very Helpful or Not Helpful at All. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

```@InProceedings{braverman_et_al:LIPIcs.ITCS.2017.18,
author =	{Braverman, Mark and Garg, Sumegha and Schvartzman, Ariel},
title =	{{Coding in Undirected Graphs Is Either Very Helpful or Not Helpful at All}},
booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
pages =	{18:1--18:18},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-029-3},
ISSN =	{1868-8969},
year =	{2017},
volume =	{67},
publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.18},
URN =		{urn:nbn:de:0030-drops-81599},
doi =		{10.4230/LIPIcs.ITCS.2017.18},
annote =	{Keywords: Network coding, Gap Amplification, Multicommodity flows}
}```
Document
Condorcet-Consistent and Approximately Strategyproof Tournament Rules

Authors: Jon Schneider, Ariel Schvartzman, and S. Matthew Weinberg

Published in: LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)

Abstract
We consider the manipulability of tournament rules for round-robin tournaments of n competitors. Specifically, n competitors are competing for a prize, and a tournament rule r maps the result of all n(n-1)/2 pairwise matches (called a tournament, T) to a distribution over winners. Rule r is Condorcet-consistent if whenever i wins all n-1 of her matches, r selects i with probability 1. We consider strategic manipulation of tournaments where player j might throw their match to player i in order to increase the likelihood that one of them wins the tournament. Regardless of the reason why j chooses to do this, the potential for manipulation exists as long as Pr[r(T) = i] increases by more than Pr[r(T) = j] decreases. Unfortunately, it is known that every Condorcet-consistent rule is manipulable. In this work, we address the question of how manipulable Condorcet-consistent rules must necessarily be - by trying to minimize the difference between the increase in Pr[r(T) = i] and decrease in Pr[r(T) = j] for any potential manipulating pair. We show that every Condorcet-consistent rule is in fact 1/3-manipulable, and that selecting a winner according to a random single elimination bracket is not alpha-manipulable for any alpha > 1/3. We also show that many previously studied tournament formats are all 1/2-manipulable, and the popular class of Copeland rules (any rule that selects a player with the most wins) are all in fact 1-manipulable, the worst possible. Finally, we consider extensions to match-fixing among sets of more than two players.

Cite as

Jon Schneider, Ariel Schvartzman, and S. Matthew Weinberg. Condorcet-Consistent and Approximately Strategyproof Tournament Rules. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 35:1-35:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

```@InProceedings{schneider_et_al:LIPIcs.ITCS.2017.35,
author =	{Schneider, Jon and Schvartzman, Ariel and Weinberg, S. Matthew},
title =	{{Condorcet-Consistent and Approximately Strategyproof Tournament Rules}},
booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
pages =	{35:1--35:20},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-029-3},
ISSN =	{1868-8969},
year =	{2017},
volume =	{67},
publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.35},
URN =		{urn:nbn:de:0030-drops-81605},
doi =		{10.4230/LIPIcs.ITCS.2017.35},
annote =	{Keywords: Tournament design, Non-manipulability, Condorcet-consistent, Strategyproofness}
}```
Document
The Fewest Clues Problem

Authors: Erik D. Demaine, Fermi Ma, Ariel Schvartzman, Erik Waingarten, and Scott Aaronson

Published in: LIPIcs, Volume 49, 8th International Conference on Fun with Algorithms (FUN 2016)

Abstract
When analyzing the computational complexity of well-known puzzles, most papers consider the algorithmic challenge of solving a given instance of (a generalized form of) the puzzle. We take a different approach by analyzing the computational complexity of designing a "good" puzzle. We assume a puzzle maker designs part of an instance, but before publishing it, wants to ensure that the puzzle has a unique solution. Given a puzzle, we introduce the FCP (fewest clues problem) version of the problem: Given an instance to a puzzle, what is the minimum number of clues we must add in order to make the instance uniquely solvable? We analyze this question for the Nikoli puzzles Sudoku, Shakashaka, and Akari. Solving these puzzles is NP-complete, and we show their FCP versions are Sigma_2^P-complete. Along the way, we show that the FCP versions of 3SAT, 1-in-3SAT, Triangle Partition, Planar 3SAT, and Latin Square are all Sigma_2^P-complete. We show that even problems in P have difficult FCP versions, sometimes even Sigma_2^P-complete, though "closed under cluing" problems are in the (presumably) smaller class NP; for example, FCP 2SAT is NP-complete.

Cite as

Erik D. Demaine, Fermi Ma, Ariel Schvartzman, Erik Waingarten, and Scott Aaronson. The Fewest Clues Problem. In 8th International Conference on Fun with Algorithms (FUN 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 49, pp. 12:1-12:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

```@InProceedings{demaine_et_al:LIPIcs.FUN.2016.12,
author =	{Demaine, Erik D. and Ma, Fermi and Schvartzman, Ariel and Waingarten, Erik and Aaronson, Scott},
title =	{{The Fewest Clues Problem}},
booktitle =	{8th International Conference on Fun with Algorithms (FUN 2016)},
pages =	{12:1--12:12},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-005-7},
ISSN =	{1868-8969},
year =	{2016},
volume =	{49},
editor =	{Demaine, Erik D. and Grandoni, Fabrizio},
publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2016.12},
URN =		{urn:nbn:de:0030-drops-58654},
doi =		{10.4230/LIPIcs.FUN.2016.12},
annote =	{Keywords: computational complexity, pencil-and-paper puzzles, hardness reductions}
}```
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