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We present a family of algorithms to solve random planted instances of any $k$-ary Boolean constraint satisfaction problem (CSP). A randomly planted instance of a Boolean CSP is generated by (1) choosing an arbitrary planted assignment…
The performance of trained neural networks is robust to harsh levels of pruning. Coupled with the ever-growing size of deep learning models, this observation has motivated extensive research on learning sparse models. In this work, we focus…
Promise Constraint Satisfaction Problems (PCSP) were proposed recently by Brakensiek and Guruswami arXiv:1704.01937 as a framework to study approximations for Constraint Satisfaction Problems (CSP). Informally a PCSP asks to distinguish…
Constraint satisfaction problems (or CSPs) have been extensively studied in, for instance, artificial intelligence, database theory, graph theory, and statistical physics. From a practical viewpoint, it is beneficial to approximately solve…
Random constraint satisfaction problems (CSPs) such as random $3$-SAT are conjectured to be computationally intractable. The average case hardness of random $3$-SAT and other CSPs has broad and far-reaching implications on problems in…
In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define…
We show that any submodular minimization (SM) problem defined on a linear constraint set with constraints having up to two variables per inequality, are 2-approximable in polynomial time. If the constraints are monotone (the two variables…
We investigate whether an n-vertex instance (G,k) of Treewidth, asking whether the graph G has treewidth at most k, can efficiently be made sparse without changing its answer. By giving a special form of OR-cross-composition, we prove that…
A discrete temporal constraint satisfaction problem is a constraint satisfaction problem (CSP) whose constraint language consists of relations that are first-order definable over $(\Bbb Z,<)$. Our main result says that every distance CSP is…
Many researchers in artificial intelligence are beginning to explore the use of soft constraints to express a set of (possibly conflicting) problem requirements. A soft constraint is a function defined on a collection of variables which…
Sparse and convolutional constraints form a natural prior for many optimization problems that arise from physical processes. Detecting motifs in speech and musical passages, super-resolving images, compressing videos, and reconstructing…
A Pseudo-Boolean (PB) constraint is a linear arithmetic constraint over Boolean variables. PB constraints are convenient and widely used in expressing NP-complete problems. We introduce a new, two step, method for transforming PB…
Promise CSPs are a relaxation of constraint satisfaction problems where the goal is to find an assignment satisfying a relaxed version of the constraints. Several well-known problems can be cast as promise CSPs including approximate graph…
A $\mu$-biased Max-CSP instance with predicate $\psi:\{0,1\}^r \to \{0,1\}$ is an instance of Constraint Satisfaction Problem (CSP) where the objective is to find a labeling of relative weight at most $\mu$ which satisfies the maximum…
We initiate the study of constraint satisfaction problems (CSPs) in the presence of counting quantifiers, which may be seen as variants of CSPs in the mould of quantified CSPs (QCSPs). We show that a single counting quantifier strictly…
In this work, we focus on the Partial Constraint Satisfaction Problem (PCSP) over control-flow graphs (CFGs) of programs. PCSP serves as a generalization of the well-known Constraint Satisfaction Problem (CSP). In the CSP framework, we…
The tractability of certain CSPs for dense or sparse instances is known from the 90s. Recently, the densification and the sparsification of CSPs were formulated as computational tasks and the systematical study of their computational…
A continuous constraint satisfaction problem (CCSP) is a constraint satisfaction problem (CSP) with an interval domain $U \subset \mathbb{R}$. We engage in a systematic study to classify CCSPs that are complete of the Existential Theory of…
A polynomial matrix inequality is a formula asserting that a polynomial matrix is positive semidefinite. Polynomial matrix optimization concerns minimizing the smallest eigenvalue of a symmetric polynomial matrix subject to a tuple of…
A Boolean constraint satisfaction instance is a conjunction of constraint applications, where the allowed constraints are drawn from a fixed set B of Boolean functions. We consider the problem of determining whether two given constraint…