Related papers: CNF Satisfiability in a Subspace and Related Probl…

The Boolean satisfiability (SAT) problem is a computationally challenging decision problem central to many industrial applications. For SAT problems in cryptanalysis, circuit design, and telecommunication, solutions can often be found more…

The main purpose of this paper is to study the NP-complete subset-sum problem, not in the usual context of time-complexity-based classification of the algorithms (exponential/polynomial), but through a new kind of algorithmic classification…

We establish the satisfiability threshold for random $k$-SAT for all $k\ge k_0$, with $k_0$ an absolute constant. That is, there exists a limiting density $\alpha_*(k)$ such that a random $k$-SAT formula of clause density $\alpha$ is with…

To any fixed, finite relational structure, $\mathbb{D}$, there is an associated decision problem, CSP$(\mathbb{D})$, which is a restricted version of the constraint satisfaction problem. In [8], the so called "algebraic approach" to the…

The problem of estimating the proportion of satisfiable instances of a given CSP (constraint satisfaction problem) can be tackled through weighting. It consists in putting onto each solution a non-negative real value based on its…

We present the current fastest deterministic algorithm for $k$-SAT, improving the upper bound $(2-2/k)^{n + o(n)}$ dues to Moser and Scheder [STOC'11]. The algorithm combines a branching algorithm with the derandomized local search, whose…

We consider the problem of approximately solving constraint satisfaction problems with arity $k > 2$ ($k$-CSPs) on instances satisfying certain expansion properties, when viewed as hypergraphs. Random instances of $k$-CSPs, which are also…

Given a collection of $m$ sets from a universe $\mathcal{U}$, the Maximum Set Coverage problem consists of finding $k$ sets whose union has largest cardinality. This problem is NP-Hard, but the solution can be approximated by a polynomial…

Network applications, such as multimedia streaming and video conferencing, impose growing requirements over Quality of Service (QoS), including bandwidth, delay, jitter, etc. Meanwhile, networks are expected to be load-balanced,…

Using powerful Multicanonical Ensemble Monte Carlo methods from statistical physics we explore the realization space of random K satisfiability (KSAT) in search for computational hard problems, most likely the 'hardest problems'. We search…

Earlier we introduced the notion of a stable set of points (SSP). We proved that a CNF formula is unsatisfiable iff there is a set of points (i.e. complete assignments) that is stable with respect to this formula. Experiments showed that…

Sequential testing problems involve a complex system with several components, each of which is "working" with some independent probability. The outcome of each component can be determined by performing a test, which incurs some cost. The…

In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…

Several continuous dynamical systems have recently been proposed as special-purpose analog computers designed to solve combinatorial optimization problems such as $k$-SAT or the Ising problem. While combinatorial optimization problems are…

The fuzzy $K$-means problem is a generalization of the classical $K$-means problem to soft clusterings, i.e. clusterings where each points belongs to each cluster to some degree. Although popular in practice, prior to this work the fuzzy…

We consider the random $k$-SAT problem with $n$ variables, $m=m(n)$ clauses, and clause density $\alpha=\lim_{n\to\infty}m/n$ for $k=2,3$. It is known that if $\alpha$ is small enough, then the random $k$-SAT problem admits a solution with…

Solving integer programs of the form $\min \{\mathbf{x} \mid A\mathbf{x} = \mathbf{b}, \mathbf{l} \leq \mathbf{x} \leq \mathbf{u}, \mathbf{x} \in \mathbb{Z}^n \}$ is, in general, $\mathsf{NP}$-hard. Hence, great effort has been put into…

A canonical result about satisfiability theory is that the 2-SAT problem can be solved in linear time, despite the NP-hardness of the 3-SAT problem. In the quantum 2-SAT problem, we are given a family of 2-qubit projectors $\Pi_{ij}$ on a…

We give a quantum algorithm to exactly solve certain problems in combinatorial optimization, including weighted MAX-2-SAT as well as problems where the objective function is a weighted sum of products of Ising variables, all terms of the…

We build on a recently proposed method for stepwise explaining solutions of Constraint Satisfaction Problems (CSP) in a human-understandable way. An explanation here is a sequence of simple inference steps where simplicity is quantified…