Related papers: Approximating Constraint Satisfaction Problems Sym…
In this work, we consider the problem of minimising the social cost in atomic congestion games. For this problem, we provide tight computational lower bounds along with taxation mechanisms yielding polynomial time algorithms with optimal…
Finite valued constraint satisfaction problems are a formalism for describing many natural optimization problems, where constraints on the values that variables can take come with rational weights and the aim is to find an assignment of…
We report (to our knowledge) the first evaluation of Constraint Satisfaction as a computational framework for solving closest string problems. We show that careful consideration of symbol occurrences can provide search heuristics that…
The Promise Constraint Satisfaction Problem (PCSP for short) is a generalization of the well-studied Constraint Satisfaction Problem (CSP). The PCSP has its roots in such classic problems as the Approximate Graph Coloring and the…
We show how two techniques from statistical physics can be adapted to solve a variant of the notorious Unique Games problem, potentially opening new avenues towards the Unique Games Conjecture. The variant, which we call Count Unique Games,…
We introduce a 2-round stochastic constraint-satisfaction problem, and show that its approximation version is complete for (the promise version of) the complexity class AM. This gives a `PCP characterization' of AM analogous to the PCP…
We study the exponential time complexity of approximate counting satisfying assignments of CNFs. We reduce the problem to deciding satisfiability of a CNF. Our reduction preserves the number of variables of the input formula and thus also…
We establish the expressibility in fixed-point logic with counting (FPC) of a number of natural polynomial-time problems. In particular, we show that the size of a maximum matching in a graph is definable in FPC. This settles an open…
The problem of computing a common point that lies in the intersection of a finite number of closed convex sets, each known to one agent in a network, is studied. This issue, known as the distributed convex feasibility problem or the…
We describe simple algebraic and combinatorial characterisations of finite relational core structures admitting finitely many obstructions. As a consequence, we show that it is decidable to determine whether a constraint satisfaction…
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, I consider a fine-grained dichotomy of Boolean counting constraint satisfaction problem (#CSP), under the exponential time hypothesis of counting version (#ETH). Suppose $\mathscr{F}$ is a finite set of algebraic…
We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…
The degree of a CSP instance is the maximum number of times that a variable may appear in the scope of constraints. We consider the approximate counting problem for Boolean CSPs with bounded-degree instances, for constraint languages…
We extend anytime constraints to the Markov game setting and the corresponding solution concept of an anytime-constrained equilibrium (ACE). Then, we present a comprehensive theory of anytime-constrained equilibria that includes (1) a…
We investigate exact semidefinite programming (SDP) relaxations for the problem of minimizing a nonconvex quadratic objective function over a feasible region defined by both finitely and infinitely many nonconvex quadratic inequality…
A predicate f:{-1,1}^k -> {0,1} with \rho(f) = \frac{|f^{-1}(1)|}{2^k} is called {\it approximation resistant} if given a near-satisfiable instance of CSP(f), it is computationally hard to find an assignment that satisfies at least…
Maximum surjective constraint satisfaction problems (Max-Sur-CSPs) are computational problems where we are given a set of variables denoting values from a finite domain B and a set of constraints on the variables. A solution to such a…
In this paper we study constrained subspace approximation problem. Given a set of $n$ points $\{a_1,\ldots,a_n\}$ in $\mathbb{R}^d$, the goal of the {\em subspace approximation} problem is to find a $k$ dimensional subspace that best…
General quadratically constrained quadratic programs (QCQPs) are challenging to solve as they are known to be NP-hard. A popular approach to approximating QCQP solutions is to use semidefinite programming (SDP) relaxations. It is well-known…