相关论文: Rounding Meets Approximate Model Counting

Due to the superiority in similarity computation and database storage for large-scale multiple modalities data, cross-modal hashing methods have attracted extensive attention in similarity retrieval across the heterogeneous modalities.…

Dell, Lapinskas and Meeks [DLM SICOMP 2022] presented a general reduction from approximate counting to decision for a class of fine-grained problems that can be viewed as hyperedge counting or detection problems in an implicit hypergraph,…

Pseudo-Boolean model counting involves computing the number of satisfying assignments of a given pseudo-Boolean (PB) formula. In recent years, PB model counting has seen increased interest partly owing to the succinctness of PB formulas…

Nearly all existing counting methods are designed for a specific object class. Our work, however, aims to create a counting model able to count any class of object. To achieve this goal, we formulate counting as a matching problem, enabling…

We consider approximation algorithms for covering integer programs of the form min $\langle c, x \rangle $ over $x \in \mathbb{N}^n $ subject to $A x \geq b $ and $x \leq d$; where $A \in \mathbb{R}_{\geq 0}^{m \times n}$, $b \in…

Inexact computing also referred to as approximate computing is a style of designing algorithms and computing systems wherein the accuracy of correctness of algorithms executing on them is deliberately traded for significant resource…

This paper considers the computer model calibration problem and provides a general frequentist solution. Under the proposed framework, the data model is semi-parametric with a nonparametric discrepancy function which accounts for any…

Chain-of-thought (CoT) prompting is necessary for arithmetic in small language models, yet shuffling its steps preserves most performance. What does CoT contribute if not logical sequencing? In three 1-3B instruction-tuned LMs on GSM8K, we…

This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum…

The approximation ratio has become one of the dominant measures in mechanism design problems. In light of analysis of algorithms, we define the \emph{smoothed approximation ratio} to compare the performance of the optimal mechanism and a…

Semidefinite programming is a powerful tool in the design and analysis of approximation algorithms for combinatorial optimization problems. In particular, the random hyperplane rounding method of Goemans and Williamson has been extensively…

In recent years, randomized methods for numerical linear algebra have received growing interest as a general approach to large-scale problems. Typically, the essential ingredient of these methods is some form of randomized dimension…

We consider approximate circular pattern matching (CPM, in short) under the Hamming and edit distance, in which we are given a length-$n$ text $T$, a length-$m$ pattern $P$, and a threshold $k>0$, and we are to report all starting positions…

This article describes a novel approach to chance-constrained programming based on the sample average approximation (SAA) method. Recent work focuses on heuristic approximations to the SAA problem and we introduce a novel approach which…

Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued…

We describe a method of model checking called Computing Range Reduction (CRR). The CRR method is based on derivation of clauses that reduce the set of traces of reachable states in such a way that at least one counterexample remains (if…

Cross-modal hashing is a successful method to solve large-scale multimedia retrieval issue. A lot of matrix factorization-based hashing methods are proposed. However, the existing methods still struggle with a few problems, such as how to…

Approximate Bayesian Computation (ABC) is a useful class of methods for Bayesian inference when the likelihood function is computationally intractable. In practice, the basic ABC algorithm may be inefficient in the presence of discrepancy…

In this paper, we consider an unconstrained optimization model where the objective is a sum of a large number of possibly nonconvex functions, though overall the objective is assumed to be smooth and convex. Our bid to solving such model…

Modern society is full of computational challenges that rely on probabilistic reasoning, statistics, and combinatorics. Interestingly, many of these questions can be formulated by encoding them into propositional formulas and then asking…