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The goal of the present paper is to prove that if a weak limit of a consistent approximation scheme of compressible complete Euler system in the full space $ \mathbb{R}^d,\; d=2,3 $ is a weak solution of the system then eventually the…

Analysis of PDEs · Mathematics 2021-09-29 Nilasis Chaudhuri

We study $n$-player turn-based games played on a finite directed graph. For each play, the players have to pay a cost that they want to minimize. Instead of the well-known notion of Nash equilibrium (NE), we focus on the notion of subgame…

Computer Science and Game Theory · Computer Science 2015-04-13 Thomas Brihaye , Véronique Bruyère , Noémie Meunier , Jean-François Raskin

We prove that computing an $\epsilon$-approximate Nash equilibrium of a win-lose bimatrix game with constant sparsity is PPAD-hard for inverse-polynomial $\epsilon$. Our result holds for 3-sparse games, which is tight given that 2-sparse…

Computational Complexity · Computer Science 2026-02-23 Eleni Batziou , John Fearnley , Abheek Ghosh , Rahul Savani

We present an approximation scheme for minimizing certain Quadratic Integer Programming problems with positive semidefinite objective functions and global linear constraints. This framework includes well known graph problems such as Minimum…

Data Structures and Algorithms · Computer Science 2013-12-12 Venkatesan Guruswami , Ali Kemal Sinop

Min-max saddle point games appear in a wide range of applications in machine leaning and signal processing. Despite their wide applicability, theoretical studies are mostly limited to the special convex-concave structure. While some recent…

Optimization and Control · Mathematics 2020-03-19 Babak Barazandeh , Meisam Razaviyayn

In this paper, we investigate the validity of the Unique Games Conjecture when the constraint graph is the boolean hypercube. We construct an almost optimal integrality gap instance on the Hypercube for the Goemans-Williamson semidefinite…

Computational Complexity · Computer Science 2014-05-07 Naman Agarwal , Guy Kindler , Alexandra Kolla , Luca Trevisan

$\delta$-Covering, for some covering range $\delta>0$, is a continuous facility location problem on undirected graphs where all edges have unit length. The facilities may be positioned on the vertices as well as on the interior of the…

Data Structures and Algorithms · Computer Science 2024-08-09 Tim A. Hartmann , Tom Janßen

We show that for every $k\in\mathbb{N}$ and $\varepsilon>0$, for large enough alphabet $R$, given a $k$-CSP with alphabet size $R$, it is NP-hard to distinguish between the case that there is an assignment satisfying at least…

Computational Complexity · Computer Science 2025-10-29 Dor Minzer , Kai Zhe Zheng

We consider multi-player graph games with partial-observation and parity objective. While the decision problem for three-player games with a coalition of the first and second players against the third player is undecidable, we present a…

Logic in Computer Science · Computer Science 2014-04-23 Krishnendu Chatterjee , Laurent Doyen

Many interactions result in a socially suboptimal equilibrium, or in a non-equilibrium state, from which arriving at an equilibrium through simple dynamics can be impossible of too long. Aiming to achieve a certain equilibrium, we persuade,…

Computer Science and Game Theory · Computer Science 2023-12-07 Gleb Polevoy , Jonas Schweichhart

We prove that any extended formulation that approximates the matching polytope on $n$-vertex graphs up to a factor of $(1+\varepsilon)$ for any $\frac2n \le \varepsilon \le 1$ must have at least $\binom{n}{{\alpha}/{\varepsilon}}$ defining…

Computational Complexity · Computer Science 2017-11-29 Makrand Sinha

In this paper we study a max-min $k$-partition problem on a weighted graph, that could model a robust $k$-coalition formation. We settle the computational complexity of this problem as complete for class $\Sigma_2^P$. This hardness holds…

Data Structures and Algorithms · Computer Science 2019-02-20 Anisse Ismaili

We prove an $N^{2-o(1)}$ lower bound on the randomized communication complexity of finding an $\epsilon$-approximate Nash equilibrium (for constant $\epsilon>0$) in a two-player $N\times N$ game.

Computational Complexity · Computer Science 2018-05-17 Mika Göös , Aviad Rubinstein

We study the problem of computing approximate Nash equilibria (epsilon-Nash equilibria) in normal form games, where the number of players is a small constant. We consider the approach of looking for solutions with constant support size. It…

Computer Science and Game Theory · Computer Science 2008-12-18 Patrick Briest , Paul W. Goldberg , Heiko Roeglin

We show a communication complexity lower bound for finding a correlated equilibrium of a two-player game. More precisely, we define a two-player $N \times N$ game called the 2-cycle game and show that the randomized communication complexity…

Computer Science and Game Theory · Computer Science 2017-04-05 Anat Ganor , Karthik C. S.

Random constraint satisfaction problems (CSPs) such as random $3$-SAT are conjectured to be computationally intractable. The average case hardness of random $3$-SAT and other CSPs has broad and far-reaching implications on problems in…

Computational Complexity · Computer Science 2019-11-11 Jonah Brown-Cohen , Prasad Raghavendra

We develop a new approach for approximating large independent sets when the input graph is a one-sided spectral expander - that is, the uniform random walk matrix of the graph has its second eigenvalue bounded away from 1. Consequently, we…

Data Structures and Algorithms · Computer Science 2024-11-07 Mitali Bafna , Jun-Ting Hsieh , Pravesh K. Kothari

In this note we provide a new proof for the results of Lipton et al. on the existence of an approximate Nash equilibrium with logarithmic support size. Besides its simplicity, the new proof leads to the following contributions: 1. For…

Computer Science and Game Theory · Computer Science 2013-05-22 Yakov Babichenko

Optimization problems consist of either maximizing or minimizing an objective function. Instead of looking for a maximum solution (resp. minimum solution), one can find a minimum maximal solution (resp. maximum minimal solution). Such…

Data Structures and Algorithms · Computer Science 2018-11-08 Kaveh Khoshkhah , Mehdi Khosravian Ghadikolaei , Jerome Monnot , Florian Sikora

We consider the problem of dividing a set of indivisible goods among agents with additive valuations. This problem has been studied under various objectives in both the computer science and the operations research literature. Our main…

Computer Science and Game Theory · Computer Science 2026-05-27 Vignesh Viswanathan