Related papers: A Method to Generate Multi-interval Pairwise Compa…
Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph.…
Interval graphs are intersection graphs of closed intervals of the real-line. The well-known computational problem, called recognition, asks whether an input graph $G$ can be represented by closed intervals, i.e., whether $G$ is an interval…
Deep generative models (DGMs) for graphs achieve impressively high expressive power thanks to very efficient and scalable neural networks. However, these networks contain non-linearities that prevent analytical computation of many standard…
Identifying clusters of similar elements in a set is a common task in data analysis. With the immense growth of data and physical limitations on single processor speed, it is necessary to find efficient parallel algorithms for clustering…
Existing genetic programming (GP) methods are typically designed based on a certain representation, such as tree-based or linear representations. These representations show various pros and cons in different domains. However, due to the…
We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we…
Ancestral sequence reconstruction is a key task in computational biology. It consists in inferring a molecular sequence at an ancestral species of a known phylogeny, given descendant sequences at the tip of the tree. In addition to its many…
In this work we consider two two-criteria optimization problems: given an input graph, the goal is to find its interval (or chordal) supergraph that minimizes the number of edges and its clique number simultaneously. For the interval…
Message Passing Neural Networks (MPNNs) are a staple of graph machine learning. MPNNs iteratively update each node's representation in an input graph by aggregating messages from the node's neighbors, which necessitates a memory complexity…
The families EPT (resp. EPG) Edge Intersection Graphs of Paths in a tree (resp. in a grid) are well studied graph classes. Recently we introduced the graph classes Edge-Intersecting and Non-Splitting Paths in a Tree ENPT, and in a Grid…
This paper is devoted to a study of single-peakedness on arbitrary graphs. Given a collection of preferences (rankings of a set of alternatives), we aim at determining a connected graph G on which the preferences are single-peaked, in the…
We present a general framework to generate trees every vertex of which has a non-negative weight and a color. The colors are used to impose certain restrictions on the weight and colors of other vertices. We first extend the enumeration…
This paper addresses the problem of determining the maximum number of edges in a unit distance graph (UDG) of $n$ vertices using computer search. An unsolved problem of Paul Erd\H{o}s asks the maximum number of edges $u(n)$ a UDG of $n$…
We introduce a new notation for representing labeled regular bipartite graphs of arbitrary degree. Several enumeration problems for labeled and unlabeled regular bipartite graphs have been introduced. A general algorithm for enumerating all…
We consider the problem of finding the smallest graph that contains two input trees each with at most $n$ vertices preserving their distances. In other words, we look for an isometric-universal graph with the minimum number of vertices for…
We study the efficient generation of random graphs with a prescribed expected degree sequence, focusing on rank-1 inhomogeneous models in which vertices are assigned weights and edges are drawn independently with probabilities proportional…
Interval graphs were used in the study of genomics by the famous molecular biologist Benzer. Later on probe interval graphs were introduced by Zhang as a generalization of interval graphs for the study of cosmid contig mapping of DNA. A…
We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. In a time series graph, each component of the vector series is represented by distinct node,…
Let $\mathcal{G}$ be the set of simple graphs (or multigraphs) $G$ such that for each $G \in \mathcal{G}$ there exists at least two non-empty disjoint proper subsets $V_{1},V_{2}\subseteq V(G)$ satisfying $V(G)\setminus(V_{1} \cup…
This paper introduces a novel hypergraph classification algorithm. The use of hypergraphs in this framework has been widely studied. In previous work, hypergraph models are typically constructed using distance or attribute based methods.…