Related papers: A Probabilistic Attack on NP-complete Problems
The hitting set problem asks for a collection of sets over a universe $U$ to find a minimum subset of $U$ that intersects each of the given sets. It is NP-hard and equivalent to the problem set cover. We give a branch-and-bound algorithm to…
Given a finite structure $M$ and property $p$, it is a natural to study the degree of satisfiability of $p$ in $M$; i.e. to ask: what is the probability that uniformly randomly chosen elements in $M$ satisfy $p$? In group theory, a…
We study the problem of query evaluation on probabilistic graphs, namely, tuple-independent probabilistic databases over signatures of arity two. We focus on the class of queries closed under homomorphisms, or, equivalently, the infinite…
In multistage perfect matching problems we are given a sequence of graphs on the same vertex set and asked to find a sequence of perfect matchings, corresponding to the sequence of graphs, such that consecutive matchings are as similar as…
Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors have phrased this problem as a nuclear norm minimization…
Checking two probabilistic automata for equivalence has been shown to be a key problem for efficiently establishing various behavioural and anonymity properties of probabilistic systems. In recent experiments a randomised equivalence test…
We investigate a correspondence between the complexity hierarchy of constraint satisfaction problems and a hierarchy of logical compactness hypotheses for finite relational structures. It seems that the harder a constraint satisfaction…
This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that…
An $n\times n\times\dots\times n$ hypercube is made from $n^d$ unit hypercubes. Two unit hypercubes are neighbours if they share a $(d-1)$-dimensional face. In each step of a dismantling process, we remove a unit hypercube that has…
We establish the geometric ergodicity of the preconditioned Hamiltonian Monte Carlo (HMC) algorithm defined on an infinite-dimensional Hilbert space, as developed in [Beskos et al., Stochastic Process. Appl., 2011]. This algorithm can be…
Many planning formalisms allow for mixing numeric with Boolean effects. However, most of these formalisms are undecidable. In this paper, we will analyze possible causes for this undecidability by studying the number of different…
Many high-dimensional statistical inference problems are believed to possess inherent computational hardness. Various frameworks have been proposed to give rigorous evidence for such hardness, including lower bounds against restricted…
We consider the problem of finding an optimal transport plan between an absolutely continuous measure $\mu$ on $\mathcal{X} \subset \mathbb{R}^d$ and a finitely supported measure $\nu$ on $\mathbb{R}^d$ when the transport cost is the…
We discuss the equivalence relation between the Euclidean bipartite matching problem on the line and on the circumference and the Brownian bridge process on the same domains. The equivalence allows us to compute the correlation function and…
In this paper we evaluate how constructive heuristics degrade when a problem transits from P to NP-hard. This is done by means of the linear ordering problem. More specifically, for this problem we prove that the objective function can be…
Computing an optimal cycle in a given homology class, also referred to as the homology localization problem, is known to be an NP-hard problem in general. Furthermore, there is currently no known optimality criterion that localizes classes…
This paper centers around two basic problems of topological coincidence theory. First, try to measure (with help of Nielsen and minimum numbers) how far a given pair of maps is from being loose, i.e. from being homotopic to a pair of…
Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…
Satisfiability checking for monotone modal logic is known to be (only) NP-complete. We show that this remains true when the logic is extended with aconjunctive and alternation-free fixpoint operators as well as the universal modality; the…
Until now, Computer Scientists have concerned themselves with identifying efficient algorithms for solving the general case of some problem -- that is finding one which performs well when the size of the input tends to infinity. In this…