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We show that various recent algorithms for finite-domain constraint satisfaction problems (CSP), which are based on solving their affine integer relaxations, do not solve all tractable and not even all Maltsev CSPs. This rules them out as…
The Constraint Satisfaction Problem (CSP) framework offers a simple and sound basis for representing and solving simple decision problems, without uncertainty. This paper is devoted to an extension of the CSP framework enabling us to deal…
Combinatorial problems stated as Constraint Satisfaction Problems (CSP) are examined. It is shown by example that any algorithm designed for the original CSP, and involving the AllDifferent constraint, has at least the same level of…
Constraint Satisfaction Problem on finite sets is known to be NP-complete in general but certain restrictions on the constraint language can ensure tractability. It was proved that if a constraint language has a weak near unanimity…
In many high-dimensional problems, like sparse-PCA, planted clique, or clustering, the best known algorithms with polynomial time complexity fail to reach the statistical performance provably achievable by algorithms free of computational…
A constraint satisfaction problem (CSP) is a computational problem where the input consists of a finite set of variables and a finite set of constraints, and where the task is to decide whether there exists a satisfying assignment of values…
We investigate the Constraint Satisfaction Problem (CSP) over templates with a group structure, and algorithms solving CSP that are equivariant, i.e. invariant under a natural group action induced by a template. Our main result is a method…
We study the approximability of two related problems on graphs with $n$ nodes and $m$ edges: $n$-Pairs Shortest Paths ($n$-PSP), where the goal is to find a shortest path between $O(n)$ prespecified pairs, and All Node Shortest Cycles…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
One specific subset of quantum algorithms is Grovers Ordered Search Problem (OSP), the quantum counterpart of the classical binary search algorithm, which utilizes oracle functions to produce a specified value within an ordered database.…
A classic result due to Schaefer (1978) classifies all constraint satisfaction problems (CSPs) over the Boolean domain as being either in $\mathsf{P}$ or $\mathsf{NP}$-hard. This paper considers a promise-problem variant of CSPs called…
For many constraint satisfaction problems, the algorithm which chooses a random assignment achieves the best possible approximation ratio. For instance, a simple random assignment for {\sc Max-E3-Sat} allows 7/8-approximation and for every…
Estimation of a vector from quantized linear measurements is a common problem for which simple linear techniques are suboptimal -- sometimes greatly so. This paper develops generalized approximate message passing (GAMP) algorithms for…
Given a graph $G$ of degree $k$ over $n$ vertices, we consider the problem of computing a near maximum cut or a near minimum bisection in polynomial time. For graphs of girth $2L$, we develop a local message passing algorithm whose…
Sparse Group LASSO (SGL) is a regularized model for high-dimensional linear regression problems with grouped covariates. SGL applies $l_1$ and $l_2$ penalties on the individual predictors and group predictors, respectively, to guarantee…
A canonical feature of the constraint satisfaction problems in NP is approximation hardness, where in the worst case, finding sufficient-quality approximate solutions is exponentially hard for all known methods. Fundamentally, the lack of…
Approximate Message Passing (AMP) is a class of iterative algorithms that have found applications in many problems in high-dimensional statistics and machine learning. In its general form, AMP can be formulated as an iterative procedure…
This paper presents a new approach for training artificial neural networks using techniques for solving the constraint satisfaction problem (CSP). The quotient gradient system (QGS) is a trajectory-based method for solving the CSP. This…
The sparse Beyesian learning (also referred to as Bayesian compressed sensing) algorithm is one of the most popular approaches for sparse signal recovery, and has demonstrated superior performance in a series of experiments. Nevertheless,…
Quantum signal processing (QSP) provides a systematic framework for implementing a polynomial transformation of a linear operator, and unifies nearly all known quantum algorithms. In parallel, recent works have developed randomized…