On Succinct Encodings for the Tournament Fixing Problem

Gupta, Sushmita; Saurabh, Saket; Sridharan, Ramanujan; Zehavi, Meirav

doi:10.24963/ijcai.2019/46

Cited by 5 publications

(6 citation statements)

References 2 publications

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“…The following lemma is very similar to Lemma 4 in (Gupta et al 2018a) (yet our notion of realizability is slightly different) as well as to lemmas given in (Ramanujan and Szeider 2017;Gupta et al 2019). Accordingly, the proof follows very similar lines, and therefore we omit it.…”

Section: Guessesmentioning

confidence: 64%

“…Afterwards, Gupta et al (Gupta et al 2018a) sped-up the aforementioned algorithm based on the use of a greedy procedure instead of ILP, and attained the currently best running time of k O(k) • n O(1) . Additionally, Gupta et al (Gupta et al 2019) proved that the problem admits a polynomial kernel with respect to k.…”

Section: Considered the Feedbackmentioning

confidence: 99%

“…Feedback Vertex Set and Our Contribution. Given the successes above for the feedback arc set number, it has been asked explicitly and repeatedly whether TOURNA-MENT FIXING is FPT also with respect to the feedback vertex set number of D (Ramanujan and Szeider 2017;Gupta et al 2018bGupta et al , 2019Roy 2020;Suksompong 2021), that is, the minimum number of nodes to remove from D in order to turn it into a DAG. Observe that the feedback vertex set number of D is always bounded from above by twice its feedback arc set number.…”

Section: Considered the Feedbackmentioning

confidence: 99%

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Tournament Fixing Parameterized by Feedback Vertex Set Number Is FPT

Zehavi

2023

AAAI

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A knockout (or single-elimination) tournament is a format of a competition that is very popular in practice (particularly in sports, elections and decision making), and which has been extensively and intensively studied from a theoretical point of view for more than a decade. Particular attention has been devoted to the Tournament Fixing problem, where, roughly speaking, the objective is to determine whether we can conduct the knockout tournament in a way that makes our favorite player win. Here, part of the input is a tournament graph D that encodes the winner of each possible match. A sequence of papers has studied the parameterized complexity of Tournament Fixing with respect to the feedback arc set number (fas) of D Given that this parameter yielded tractability, it has been asked explicitly and repeatedly whether Tournament Fixing is FPT also with respect to the feedback vertex set number (fvs) of D. We answer this question positively. In fact, although fvs can be arbitrarily smaller than fas, we attain the same dependency on the parameter in the time complexity. So, additionally, our work subsumes the best known algorithm for Tournament Fixing with respect to as.

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Section: Guessesmentioning

confidence: 64%

Section: Considered the Feedbackmentioning

confidence: 99%

Section: Considered the Feedbackmentioning

confidence: 99%

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Tournament Fixing Parameterized by Feedback Vertex Set Number Is FPT

Zehavi

2023

AAAI

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“…In particular, when the aforementioned information is deterministic and complete (i.e., for every possible match involving two players, we "know" who will be the winner) and our only influence on the competition is by picking the seeding, the problem is known as the TOURNAMENT FIXING problem. This problem and its various variations have been extensively studied from the viewpoints of classical complexity, parameterized complexity, and structural analysis (see, e.g., (Gupta et al 2019(Gupta et al , 2018aKim and Williams 2015;Aziz et al 2018;Vu, Altman, and Shoham 2009;Williams 2010;Zehavi 2023;Ramanujan and Szeider 2017;Stanton and Williams 2011b,a;Kim, Suksompong, and Williams 2017;Manurangsi and Suksompong 2023); this list is illustrative rather than comprehensive).…”

Section: Introductionmentioning

confidence: 99%

How to Make Knockout Tournaments More Popular?

Chaudhary,

Molter,

Zehavi

2024

AAAI

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Given a mapping from a set of players to the leaves of a complete binary tree (called a seeding), a knockout tournament is conducted as follows: every round, every two players with a common parent compete against each other, and the winner is promoted to the common parent; then, the leaves are deleted. When only one player remains, it is declared the winner. This is a popular competition format in sports, elections, and decision-making. Over the past decade, it has been studied intensively from both theoretical and practical points of view. Most frequently, the objective is to seed the tournament in a way that ``assists'' (or even guarantees) some particular player to win the competition. We introduce a new objective, which is very sensible from the perspective of the directors of the competition: maximize the profit or popularity of the tournament. Specifically, we associate a ``score'' with every possible match, and aim to seed the tournament to maximize the sum of the scores of the matches that take place. We focus on the case where we assume a total order on the players' strengths, and provide a wide spectrum of results on the computational complexity of the problem.

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“…This model has already been the subject of numerous papers in the last few years. Besides being independently interesting from a structural and algorithmic perspective as shown by (Vassilevska Williams 2010;Aziz et al 2014;Ramanujan and Szeider 2017;Gupta et al 2018Gupta et al , 2019Manurangsi and Suksompong 2023;Zehavi 2023), the deterministic model naturally captures sequential majority elections along binary trees (Lang et al 2007;Vu, Altman, and Shoham 2009) where each "match" is a comparison of votes of two candidates and the candidate with more votes wins and moves on.…”

Section: Introductionmentioning

confidence: 99%

An Exercise in Tournament Design: When Some Matches Must Be Scheduled

Gupta,

Sridharan,

Strulo

2024

AAAI

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Single-elimination (SE) tournaments are a popular format used in competitive environments and decision making. Algorithms for SE tournament manipulation have been an active topic of research in recent years. In this paper, we initiate the algorithmic study of a novel variant of SE tournament manipulation that aims to model the fact that certain matchups are highly desired in a sporting context, incentivizing an organizer to manipulate the bracket to make such matchups take place. We obtain both hardness and tractability results. We show that while the problem of computing a bracket enforcing a given set of matches in an SE tournament is NP-hard, there are natural restrictions that lead to polynomial-time solvability. In particular, we show polynomial-time solvability if there is a linear ordering on the ability of players with only a constant number of exceptions where a player with lower ability beats a player with higher ability.

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On Succinct Encodings for the Tournament Fixing Problem

Cited by 5 publications

References 2 publications

Tournament Fixing Parameterized by Feedback Vertex Set Number Is FPT

Tournament Fixing Parameterized by Feedback Vertex Set Number Is FPT

How to Make Knockout Tournaments More Popular?

An Exercise in Tournament Design: When Some Matches Must Be Scheduled

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