Related papers: Unique Games on the Hypercube

We consider the problem of solving random parity games. We prove that parity games exibit a phase transition threshold above $d_P$, so that when the degree of the graph that defines the game has a degree $d > d_P$ then there exists a…

This paper develops a unified framework for zero-sum games in which both the pure strategies and the payoff matrices contain complex-valued entries. By leveraging a linear isomorphism between complex and real vector spaces, we extend key…

Goemans and Williamson designed a 0.878-approximation algorithm for Max-Cut in undirected graphs [JACM'95]. Khot, Kindler, Mosel, and O'Donnel showed that the approximation ratio of the Goemans-Williamson algorithm is optimal assuming…

In scheduling and timetabling applications, the mutual-exclusion constraint stipulates that certain pairs of tasks that cannot be executed at the same time. This corresponds to the vertex colouring problem in graph theory, for which there…

We consider both finite-state game graphs and recursive game graphs (or pushdown game graphs), that can model the control flow of sequential programs with recursion, with multi-dimensional mean-payoff objectives. In pushdown games two types…

This paper develops an algorithm for upper- and lower-bounding the value function for a class of linear time-varying games subject to convex control sets. In particular, a two-player zero-sum differential game is considered where the…

We consider two-player games played on weighted directed graphs with mean-payoff and total-payoff objectives, two classical quantitative objectives. While for single-dimensional games the complexity and memory bounds for both objectives…

The results of Raghavendra (2008) show that assuming Khot's Unique Games Conjecture (2002), for every constraint satisfaction problem there exists a generic semi-definite program that achieves the optimal approximation factor. This result…

In this paper, we prove an almost-optimal hardness for Max $k$-CSP$_R$ based on Khot's Unique Games Conjecture (UGC). In Max $k$-CSP$_R$, we are given a set of predicates each of which depends on exactly $k$ variables. Each variable can…

A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum…

We present a polynomial-time reduction from max-plus-average constraints to the feasibility problem for semidefinite programs. This shows that Condon's simple stochastic games, stochastic mean payoff games, and in particular mean payoff…

An approximation algorithm for a constraint satisfaction problem is called robust if it outputs an assignment satisfying a $(1 - f(\epsilon))$-fraction of the constraints on any $(1-\epsilon)$-satisfiable instance, where the loss function…

The Gaussian noise stability of a function $f:\mathbb{R}^n \to \{-1, 1\}$ is the expected value of $f(\boldsymbol{x}) \cdot f(\boldsymbol{y})$ over $\rho$-correlated Gaussian random variables $\boldsymbol{x}$ and $\boldsymbol{y}$. Borell's…

With the increasing sophistication of attacks on cyber-physical systems, deception has emerged as an effective tool to improve system security and safety by obfuscating the attacker's perception. In this paper, we present a solution to the…

The problem of finding a maximum $2$-matching without short cycles has received significant attention due to its relevance to the Hamilton cycle problem. This problem is generalized to finding a maximum $t$-matching which excludes specified…

This paper considers a formulation of a differential game with constrained dynamics, where one player selects the dynamics and the other selects the applicable cost. When the game is considered on a finite time horizon, its value satisfies…

Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…

We study linear constraint system (LCS) games over the ring of arithmetic modulo $d$. We give a new proof that certain LCS games (the Mermin--Peres Magic Square and Magic Pentagram over binary alphabets, together with parallel repetitions…

The paper is concerned with two-person dynamic zero-sum games. We investigate the limit of value functions of finite horizon games with long run average cost as the time horizon tends to infinity, and the limit of value functions of…

We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…