Related papers: Computational topology and the Unique Games Conjec…
We establish relationships between various topological selection games involving the space of minimal cusco maps into the real line and the underlying domain. These connections occur across different topologies, including the topology of…
Topological fixpoint logics are a family of logics that admits topological models and where the fixpoint operators are defined with respect to the topological interpretations. Here we consider a topological fixpoint logic for relational…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
We develop an algebraic and operational framework for quantum isomorphisms of hypergraphs, using tools from compact quantum group theory. We introduce a new synchronous version of the hypergraph isomorphism game whose game algebra uniformly…
The class of exact transferable utility coalitional games, introduced in 1972 by Schmeidler, has been studied both in the context of game theory and in the context of imprecise probabilities. We characterize the cone of exact games by…
We give a new algorithm for Unique Games which is based on purely {\em spectral} techniques, in contrast to previous work in the area, which relies heavily on semidefinite programming (SDP). Given a highly satisfiable instance of Unique…
We study two-player concurrent stochastic games on finite graphs, with B\"uchi and co-B\"uchi objectives. The goal of the first player is to maximize the probability of satisfying the given objective. Following Martin's determinacy theorem…
Consider a situation with $n$ agents or players where some of the players form a coalition with a certain collective objective. Simple games are used to model systems that can decide whether coalitions are successful (winning) or not…
We investigate a phenomenon of "one-to-two-player lifting" in infinite-duration two-player games on graphs with zero-sum objectives. More specifically, let $C$ be a class of strategies. It turns out that in many cases, to show that all…
The classic paper of Shapley and Shubik \cite{Shapley1971assignment} characterized the core of the assignment game using ideas from matching theory and LP-duality theory and their highly non-trivial interplay. Whereas the core of this game…
The game of Cops and Robber is traditionally played on a finite graph. The purpose of this note is to introduce and analyze the game that is played on an arbitrary geodesic space. The game is defined in such a way that it preserves the…
We study unique games and estimate some of their values. We prove that if a unique game has a quantum-assisted value close to 1, then it must have a perfect deterministic strategy. We introduce a family of unique games based on groups that…
We initiate the study of simple games from the point of view of combinatorial topology. The starting premise is that the losing coalitions of a simple game can be identified with a simplicial complex. Various topological constructions and…
The vertex cover problem is a famous combinatorial problem, and its complexity has been heavily studied. While a 2-approximation can be trivially obtained for it, researchers have not been able to approximate it better than 2-\textit{o}(1).…
In 2003, Fischermann et al. considered the maximum size of \textit{uniquely-dominatable} graphs, graphs whose dominating number is realized only by a unique dominating set. They conjectured a size bound and provide a general graph…
In this paper we connect selection principles on a topological space to corresponding selection principles on one of its hyperspaces. We unify techniques and generalize theorems from the known results about selection principles for common…
In this paper, we study the average case complexity of the Unique Games problem. We propose a natural semi-random model, in which a unique game instance is generated in several steps. First an adversary selects a completely satisfiable…
An $n$-player game $X$ in normal form can be modeled via undirected discrete graphical models where the discrete random variables represent the players and their state spaces are the set of pure strategies. There exists an edge between the…
Many packing, scheduling and covering problems that were previously considered by computer science literature in the context of various transportation and production problems, appear also suitable for describing and modeling various…
Assuming the Unique Games Conjecture, we show strong inapproximability results for two natural vertex deletion problems on directed graphs: for any integer $k\geq 2$ and arbitrary small $\epsilon > 0$, the Feedback Vertex Set problem and…