Related papers: Lower Bound for the Unique Games Problem
Weighted timed games are played by two players on a timed automaton equipped with weights: one player wants to minimise the accumulated weight while reaching a target, while the other has an opposite objective. Used in a reactive synthesis…
Parity games are abstract infinite-round games that take an important role in formal verification. In the basic setting, these games are two-player, turn-based, and played under perfect information on directed graphs, whose nodes are…
We develop an experimental algorithm for the exact solving of the maximum independent set problem. The algorithm consecutively finds the maximal independent sets of vertices in an arbitrary undirected graph such that the next such set…
We develop a polynomial time $\Omega\left ( \frac 1R \log R \right)$ approximate algorithm for Max 2CSP-$R$, the problem where we are given a collection of constraints, each involving two variables, where each variable ranges over a set of…
Graph games provide the foundation for modeling and synthesis of reactive processes. Such games are played over graphs where the vertices are controlled by two adversarial players. We consider graph games where the objective of the first…
We consider the NP-hard problem of MAP-inference for undirected discrete graphical models. We propose a polynomial time and practically efficient algorithm for finding a part of its optimal solution. Specifically, our algorithm marks some…
In this paper, we study a game with positive or plus infinite expectation and determine the optimal proportion of investment for maximizing the limit expectation of growth rate per attempt. With this objective, we introduce a new pricing…
The maximum independent set problem is one of the most important problems in graph algorithms and has been extensively studied in the line of research on the worst-case analysis of exact algorithms for NP-hard problems. In the weighted…
The graph partition problem is the problem of partitioning the vertex set of a graph into a fixed number of sets of given sizes such that the sum of weights of edges joining different sets is optimized. In this paper we simplify a known…
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…
We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation…
We consider a variant of the clustering problem for a complete weighted graph. The aim is to partition the nodes into clusters maximizing the sum of the edge weights within the clusters. This problem is known as the clique partitioning…
We establish essentially optimal bounds on the complexity of initial-value problems in the randomized and quantum settings. For this purpose we define a sequence of new algorithms whose error/cost properties improve from step to step. These…
We define a class of zero-sum games with combinatorial structure, where the best response problem of one player is to maximize a submodular function. For example, this class includes security games played on networks, as well as the problem…
The restricted max-min fair allocation problem seeks an allocation of resources to players that maximizes the minimum total value obtained by any player. It is NP-hard to approximate the problem to a ratio less than 2. Comparing the current…
We investigate the problem of sequentially predicting the binary labels on the nodes of an arbitrary weighted graph. We show that, under a suitable parametrization of the problem, the optimal number of prediction mistakes can be…
An average-time game is played on the infinite graph of configurations of a finite timed automaton. The two players, Min and Max, construct an infinite run of the automaton by taking turns to perform a timed transition. Player Min wants to…
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…
The optimization version of the Unique Label Cover problem is at the heart of the Unique Games Conjecture which has played an important role in the proof of several tight inapproximability results. In recent years, this problem has been…
We consider the problem of designing a linear program that has diverse solutions as the right-hand side varies. This problem arises in video game settings where designers aim to have players use different "weapons" or "tactics" as they…