Related papers: Constraint Satisfaction Programming for the No-thr…

We propose an algorithm for general nonlinear conic programming which does not require the knowledge of the full cone, but rather a simpler, more tractable, approximation of it. We prove that the algorithm satisfies a strong global…

The Minimum Spanning Tree with Conflicting Edge Pairs is a generalization that adds conflict constraints to a classical optimization problem on graphs used to model several real-world applications. In the last few years several approaches,…

We consider the problem of estimating the locations of a set of points in a k-dimensional euclidean space given a subset of the pairwise distance measurements between the points. We focus on the case when some fraction of these measurements…

For a large number of random constraint satisfaction problems, such as random k-SAT and random graph and hypergraph coloring, there are very good estimates of the largest constraint density for which solutions exist. Yet, all known…

We lower bound the complexity of finding $\epsilon$-stationary points (with gradient norm at most $\epsilon$) using stochastic first-order methods. In a well-studied model where algorithms access smooth, potentially non-convex functions…

In this work we count the number of satisfying states of triangulations of a convex n-gon using the transfer matrix method. We show an exponential (in n) lower bound. We also give the exact formula for the number of satisfying states of a…

We find an orientation of a tree with 20 vertices such that the corresponding fixed-template constraint satisfaction problem (CSP) is NP-complete, and prove that for every orientation of a tree with fewer vertices the corresponding CSP can…

We consider worst case time bounds for NP-complete problems including 3-SAT, 3-coloring, 3-edge-coloring, and 3-list-coloring. Our algorithms are based on a constraint satisfaction (CSP) formulation of these problems. 3-SAT is equivalent to…

This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…

The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…

The best known size lower bounds against unrestricted circuits have remained around $3n$ for several decades. Moreover, the only known technique for proving lower bounds in this model, gate elimination, is inherently limited to proving…

The 3-domatic number problem asks whether a given graph can be partitioned intothree dominating sets. We prove that this problem can be solved by a deterministic algorithm in time 2.695^n (up to polynomial factors). This result improves the…

Disjointly constrained multilinear programming concerns the problem of maximizing a multilinear function on the product of finitely many disjoint polyhedra. While maximizing a linear function on a polytope (linear programming) is known to…

Enforcing constraint satisfaction in neural network outputs is critical for safety, reliability, and physical fidelity in many control and decision-making applications. While soft-constrained methods penalize constraint violations during…

For $n\geq 3$, let $(H_n, E)$ denote the $n$-th Henson graph, i.e., the unique countable homogeneous graph with exactly those finite graphs as induced subgraphs that do not embed the complete graph on $n$ vertices. We show that for all…

We propose faster algorithms for the following three optimization problems on $n$ collinear points, i.e., points in dimension one. The first two problems are known to be NP-hard in higher dimensions. 1- Maximizing total area of disjoint…

Given a set $P$ of $n$ points that are moving in the plane, we consider the problem of computing a spanning tree for these moving points that does not change its combinatorial structure during the point movement. The objective is to…

This paper analyzes to what extent it is possible to efficiently reduce the number of clauses in NP-hard satisfiability problems, without changing the answer. Upper and lower bounds are established using the concept of kernelization.…

We use a dynamic programming algorithm to establish a lower bound on the domination number of complete grid graphs of the form $C_n\square P_m$, that is, the Cartesian product of a cycle $C_n$ and a path $P_m$, for $m$ and $n$ sufficiently…

In this paper, we shed new light on the spectrum of the relation algebra we call $A_{n}$, which is obtained by splitting the non-flexible diversity atom of $6_{7}$ into $n$ symmetric atoms. Precisely, we show that the minimum value in…