相关论文: Deriving differential approximation results for $k…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
This thesis investigates the extent to which the optimal value of a constraint satisfaction problem (CSP) can be approximated by some sentence of fixed point logic with counting (FPC). It is known that, assuming $\mathsf{P} \neq…
We give a simple combinatorial algorithm to deterministically approximately count the number of satisfying assignments of general constraint satisfaction problems (CSPs). Suppose that the CSP has domain size $q=O(1)$, each constraint…
Submodular maximization is one of the central topics in combinatorial optimization. It has found numerous applications in the real world. In the past decades, a series of algorithms have been proposed for this problem. However, most of the…
Determinantal Point Processes (DPPs) are elegant probabilistic models of repulsion and diversity over discrete sets of items. But their applicability to large sets is hindered by expensive cubic-complexity matrix operations for basic tasks…
Compound distributions allow construction of a rich set of distributions. Typically they involve an intractable integral. Here we use a quadrature approximation to that integral to define the quadrature compound family. Special care is…
The distance from calibration, introduced by B{\l}asiok, Gopalan, Hu, and Nakkiran (STOC 2023), has recently emerged as a central measure of miscalibration for probabilistic predictors. We study the fundamental problems of computing and…
We study approximation algorithms for satisfiable and nearly satisfiable instances of ordering constraint satisfaction problems (ordering CSPs). Ordering CSPs arise naturally in ranking and scheduling, yet their approximability remains…
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…
We study the computational complexity of several problems connected with finding a maximal distance-$k$ matching of minimum cardinality or minimum weight in a given graph. We introduce the class of $k$-equimatchable graphs which is an edge…
We compute averages of products and ratios of characteristic polynomials associated with Orthogonal, Unitary, and Symplectic Ensembles of Random Matrix Theory. The pfaffian/determinantal formulas for these averages are obtained, and the…
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…
A linear code with parameters $[n, k, n - k + 1]$ is called maximum distance separable (MDS), and one with parameters $[n, k, n - k]$ is called almost MDS (AMDS). A code is near-MDS (NMDS) if both it and its dual are AMDS. NMDS codes…
Popular deterministic approximations of posterior distributions from, e.g. the Laplace method, variational Bayes and expectation-propagation, generally rely on symmetric approximating families, often taken to be Gaussian. This choice…
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…
Connected clustering denotes a family of constrained clustering problems in which we are given a distance metric and an undirected connectivity graph $G$ that can be completely unrelated to the metric. The aim is to partition the $n$…
We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…
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.…
The Constraint Satisfaction Problem (CSP) and its counting counterpart appears under different guises in many areas of mathematics, computer science, and elsewhere. Its structural and algorithmic properties have demonstrated to play a…
Chance constrained programming (CCP) refers to a type of optimization problem with uncertain constraints that are satisfied with at least a prescribed probability level. In this work, we study the sample average approximation (SAA) of…