Related papers: On Hashing-Based Approaches to Approximate DNF-Cou…

Model counting of Disjunctive Normal Form (DNF) formulas is a critical problem in applications such as probabilistic inference and network reliability. For example, it is often used for query evaluation in probabilistic databases. Due to…

Weighted model counting (WMC) consists of computing the weighted sum of all satisfying assignments of a propositional formula. WMC is well-known to be #P-hard for exact solving, but admits a fully polynomial randomized approximation scheme…

Given a CNF formula F on n variables, the problem of model counting or #SAT is to compute the number of satisfying assignments of F . Model counting is a fundamental but hard problem in computer science with varied applications. Recent…

Constrained counting and sampling are two fundamental problems in Computer Science with numerous applications, including network reliability, privacy, probabilistic reasoning, and constrained-random verification. In constrained counting,…

Inference in probabilistic logic languages such as ProbLog, an extension of Prolog with probabilistic facts, is often based on a reduction to a propositional formula in DNF. Calculating the probability of such a formula involves the…

Weighted model counting (WMC) has emerged as a prevalent approach for probabilistic inference. In its most general form, WMC is #P-hard. Weighted DNF counting (weighted #DNF) is a special case, where approximations with probabilistic…

Conjunctive queries are one of the most common class of queries used in database systems, and the best studied in the literature. A seminal result of Grohe, Schwentick, and Segoufin (STOC 2001) demonstrates that for every class $G$ of…

Query evaluation over probabilistic databases is notoriously intractable -- not only in combined complexity, but often in data complexity as well. This motivates the study of approximation algorithms, and particularly of combined FPRASes,…

Constrained counting is important in domains ranging from artificial intelligence to software analysis. There are already a few approaches for counting models over various types of constraints. Recently, hashing-based approaches achieve…

Counting problems are fundamental across mathematics and computer science. Among the most subtle are those whose associated decision problem is solvable in polynomial time, yet whose exact counting version appears intractable. For some such…

Neural Architecture Search (NAS) technologies have emerged in many domains to jointly learn the architectures and weights of the neural network. However, most existing NAS works claim they are task-specific and focus only on optimizing a…

In recent years, Deep Neural Networks (DNN) based methods have achieved remarkable performance in a wide range of tasks and have been among the most powerful and widely used techniques in computer vision. However, DNN-based methods are both…

To tackle the exponentiality associated with NP-hard problems, two paradigms have been proposed. First, Branch & Bound, like Dynamic Programming, achieve efficient exact inference but requires extensive information and analysis about the…

Recent years have seen more and more demand for a unified framework to address multiple realistic image retrieval tasks concerning both category and attributes. Considering the scale of modern datasets, hashing is favorable for its low…

We (claim to) prove the extremely surprising fact that NP=RP. It is achieved by creating a Fully Polynomial-Time Randomized Approximation Scheme (FPRAS) for approximately counting the number of independent sets in bounded degree graphs,…

Approximate Nearest Neighbor Search (ANNS) is a fundamental problem in many areas of machine learning and data mining. During the past decade, numerous hashing algorithms are proposed to solve this problem. Every proposed algorithm claims…

We study the approximability of the four-vertex model, a special case of the six-vertex model.We prove that, despite being NP-hard to approximate in the worst case, the four-vertex model admits a fully polynomial randomized approximation…

Model counting is the problem of computing the number of satisfying assignments of a given propositional formula. Although exact model counters can be naturally furnished by most of the knowledge compilation (KC) methods, in practice, they…

Deep hashing enables image retrieval by end-to-end learning of deep representations and hash codes from training data with pairwise similarity information. Subject to the distribution skewness underlying the similarity information, most…

In this paper we introduce a new approach for approximately counting in bounded degree systems with higher-order constraints. Our main result is an algorithm to approximately count the number of solutions to a CNF formula $\Phi$ when the…