Related papers: Chordal Graphs in Triangular Decomposition in Top-…
Finding dense subgraphs of a large graph is a standard problem in graph mining that has been studied extensively both for its theoretical richness and its many practical applications. In this paper we introduce a new family of dense…
We study the graph signal denoising problem by estimating a piecewise constant signal over an undirected graph. We propose a new Bayesian approach that first converts a general graph to a chain graph via the depth-first search algorithm,…
In this article we use the modular decomposition technique for exact solving the weighted maximum clique problem. Our algorithm takes the modular decomposition tree from the paper of Tedder et. al. and finds solution recursively. Also, we…
We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such a technique consists in a specific scaling similarity transformation that reduces…
Minimizing a sum of simple submodular functions of limited support is a special case of general submodular function minimization that has seen numerous applications in machine learning. We develop fast techniques for instances where…
Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…
Containing many classic optimization problems, the family of vertex deletion problems has an important position in algorithm and complexity study. The celebrated result of Lewis and Yannakakis gives a complete dichotomy of their complexity.…
Carleson and sparse collections of sets play a central role in dyadic harmonic analysis. We employ methods from optimization theory to study such collections. First, we present a strongly polynomial algorithm to compute the Carleson…
We consider the problem of learning a causal graph over a set of variables with interventions. We study the cost-optimal causal graph learning problem: For a given skeleton (undirected version of the causal graph), design the set of…
Understanding feature-outcome associations in high-dimensional data remains challenging when relationships vary across subpopulations, yet standard methods assuming global associations miss context-dependent patterns, reducing statistical…
We design a critically-sampled compact-support biorthogonal transform for graph signals, via graph filterbanks. Instead of partitioning the nodes in two sets so as to remove one every two nodes in the filterbank downsampling operations, the…
In matching theory, one of the most fundamental and classical branches of combinatorics, {\em canonical decompositions} of graphs are powerful and versatile tools that form the basis of this theory. However, the abilities of the known…
A plane near-triangulation G can be decomposed into a collection of induced subgraphs, described here as the W-components of G, such that G is perfect (respectively, chordal) if and only if each of its W-components is perfect (respectively,…
In this paper, we consider the problem of partitioning a polygon into a set of connected disjoint sub-polygons, each of which covers an area of a specific size. The work is motivated by terrain covering applications in robotics, where the…
We propose principled Gaussian processes (GPs) for modeling functions defined over the edge set of a simplicial 2-complex, a structure similar to a graph in which edges may form triangular faces. This approach is intended for learning…
$k$-truss model is a typical cohesive subgraph model and has been received considerable attention recently. However, the $k$-truss model only considers the direct common neighbors of an edge, which restricts its ability to reveal…
Geometric graphs form an important family of hidden structures behind data. In this paper, we develop an efficient and robust algorithm to infer a graph skeleton of a high-dimensional point cloud dataset (PCD). Previously, there has been…
Given an approximation to a multiple isolated solution of a polynomial system of equations, we have provided a symbolic-numeric deflation algorithm to restore the quadratic convergence of Newton's method. Using first-order derivatives of…
High triangle density -- the graph property stating that a constant fraction of two-hop paths belong to a triangle -- is a common signature of social networks. This paper studies triangle-dense graphs from a structural perspective. We prove…
The generalized composition graph is used by Cardoso and some researchers for factorization of the adjacency spectrum and Laplacian of a simple graph. Because the generalized composition graph is an example of a set-theoretic linear operad,…