Related papers: Catching the k-NAESAT Threshold
In the minimum $k$-edge-connected spanning subgraph ($k$-ECSS) problem the goal is to find the minimum weight subgraph resistant to up to $k-1$ edge failures. This is a central problem in network design, and a natural generalization of the…
Numerical analysis has no satisfactory method for the more realistic optimization models. However, with constraint programming one can compute a cover for the solution set to arbitrarily close approximation. Because the use of constraint…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…
This paper describes an extension to the constraint satisfaction problem (CSP) called MUSE CSP (MUltiply SEgmented Constraint Satisfaction Problem). This extension is especially useful for those problems which segment into multiple sets of…
In this paper, we consider stochastic monotone Nash games where each player's strategy set is characterized by possibly a large number of explicit convex constraint inequalities. Notably, the functional constraints of each player may depend…
We prove bounds for the number of solutions to $$a_1 + \dots + a_k = a_1' + \dots + a_k'$$ over $N$-element sets of reals, which are sufficiently convex or near-convex. A near-convex set will be the image of a set with small additive…
Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. The worst-case hardness of SAT lies at the core of computational complexity theory. The average-case analysis of SAT has triggered the…
Constraint satisfaction problems (CSPs) consist of a set of variables taking values from some finite domain and a set of local constraints on these variables. The objective is to find an assignment to the variables that maximizes the…
Many geophysical problems can be cast as inverse problems that estimate a set of parameter values from observed data. Within a Bayesian framework, solutions to such problems are described probabilistically by the so-called posterior…
The problem of non-monotone $k$-submodular maximization under a knapsack constraint ($\kSMK$) over the ground set size $n$ has been raised in many applications in machine learning, such as data summarization, information propagation, etc.…
We develop constrained Bayesian estimation methods for small area problems: those requiring smoothness with respect to similarity across areas, such as geographic proximity or clustering by covariates; and benchmarking constraints,…
We define a novel notion of ``non-backtracking'' matrix associated to any symmetric matrix, and we prove a ``Ihara-Bass'' type formula for it. We use this theory to prove new results on polynomial-time strong refutations of random…
We consider the regular balanced model of formula generation in conjunctive normal form (CNF) introduced by Boufkhad, Dubois, Interian, and Selman. We say that a formula is $p$-satisfying if there is a truth assignment satisfying…
The contention resolution framework is a versatile rounding technique used as a part of the relaxation and rounding approach for solving constrained submodular function maximization problems. We apply this framework to the hypergraph…
We present an algorithm for strongly refuting smoothed instances of all Boolean CSPs. The smoothed model is a hybrid between worst and average-case input models, where the input is an arbitrary instance of the CSP with only the negation…
Given a set of points, clustering consists of finding a partition of a point set into $k$ clusters such that the center to which a point is assigned is as close as possible. Most commonly, centers are points themselves, which leads to the…
Existing approaches remain largely constrained by traditional distance metrics, limiting their effectiveness in handling random data. In this work, we introduce the first k-means variant in the literature that operates within a…
The overlapping coefficient is a fundamental measure of similarity between probability distributions. While the case of two distributions has been extensively studied, extending this measure to multiple populations presents both analytical…
In a $(k,2)$-Constraint Satisfaction Problem we are given a set of arbitrary constraints on pairs of $k$-ary variables, and are asked to find an assignment of values to these variables such that all constraints are satisfied. The…
Probability density estimation is a core problem of statistics and signal processing. Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severely…