相关论文: Exploring the Use of Shatter for AllSAT Through Ra…

The computational cost of counting the number of solutions satisfying a Boolean formula, which is a problem instance of #SAT, has proven subtle to quantify. Even when finding individual satisfying solutions is computationally easy (e.g.…

Many differentially private and classical non-private graph algorithms rely crucially on determining whether some property of each vertex meets a threshold. For example, for the $k$-core decomposition problem, the classic peeling algorithm…

In this growing age of data and technology, large black-box models are becoming the norm due to their ability to handle vast amounts of data and learn incredibly complex data patterns. The deficiency of these methods, however, is their…

In this paper we discuss the theory used in the design of an open source lightmorphic signatures analysis toolkit (LSAT). In addition to providing a core functionality, the software package enables specific optimizations with its modular…

Many challenging Graver bases computations, like for multi-way tables in statistics, have a highly symmetric problem structure that is not exploited so far computationally. In this paper we present a Graver basis algorithm for sublattices…

Given a graph $H$, let $\chi_H(\mathbb{R}^n)$ be the smallest positive integer $r$ such that there exists an $r$-coloring of $\mathbb{R}^n$ with no monochromatic unit-copy of $H$, that is a set of $|V(H)|$ vertices of the same color such…

SATNet is a differentiable constraint solver with a custom backpropagation algorithm, which can be used as a layer in a deep-learning system. It is a promising proposal for bridging deep learning and logical reasoning. In fact, SATNet has…

Several challenging problem in clustering, partitioning and imaging have traditionally been solved using the "spectral technique". These problems include the normalized cut problem, the graph expander ratio problem, the Cheeger constant…

A construction described by the current author in 2017 uses two linear `prototype' graphs to build a compound graph with Ramsey properties inherited from the prototypes. This paper describes a generalisation of that construction which has…

In this paper we introduce a new clustering technique called Regularity Clustering. This new technique is based on the practical variants of the two constructive versions of the Regularity Lemma, a very useful tool in graph theory. The…

Gallai-colorings are edge-colored complete graphs in which there are no rainbow triangles. Within such colored complete graphs, we consider Ramsey-type questions, looking for specified monochromatic graphs. In this work, we consider…

Spectral Clustering is one of the most traditional methods to solve segmentation problems. Based on Normalized Cuts, it aims at partitioning an image using an objective function defined by a graph. Despite their mathematical attractiveness,…

Objective: Shapley additive explanations (SHAP) is a popular post-hoc technique for explaining black box models. While the impact of data imbalance on predictive models has been extensively studied, it remains largely unknown with respect…

Few-shot learning (FSL), purposing to resolve the problem of data-scarce, has attracted considerable attention in recent years. A popular FSL framework contains two phases: (i) the pre-train phase employs the base data to train a CNN-based…

Discrete variables are common in many applications, such as probabilistic reasoning, planning and explainable AI. When symbolic reasoning techniques are brought in to bear on these applications, a standard technique for handling discrete…

Feature extraction is a fundamental task in the application of machine learning methods to SAT solving. It is used in algorithm selection and configuration for solver portfolios and satisfiability classification. Many approaches have been…

In this work, we present a novel technique for GPU-accelerated Boolean satisfiability (SAT) sampling. Unlike conventional sampling algorithms that directly operate on conjunctive normal form (CNF), our method transforms the logical…

The problem of substructure characteristic modes is developed using a scattering matrix-based formulation, generalizing subregion characteristic mode decomposition to arbitrary computational tools. It is shown that the modes of the…

In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…

We study a broad class of algorithmic problems with an "additive flavor" such as computing sumsets, 3SUM, Subset Sum and geometric pattern matching. Our starting point is that these problems can often be solved efficiently for integers,…