Related papers: Brute-force search and Warshall algorithms for mat…
In the matching interdiction problem, we are given an undirected graph with weights and interdiction costs on the edges and seek to remove a subset of the edges constrained to some budget, such that the weight of a maximum weight matching…
Suppose a target is hidden in one of the vertices of an edge-weighted graph according to a known probability distribution. The expanding search problem asks for a search sequence of the vertices so as to minimize the expected time for…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
In earlier work the Kauffman bracket polynomial was extended to an invariant of marked graphs, i.e., looped graphs whose vertices have been partitioned into two classes (marked and not marked). The marked-graph bracket polynomial is readily…
We consider the problem of graph searching with prediction recently introduced by Banerjee et al. (2022). In this problem, an agent, starting at some vertex $r$ has to traverse a (potentially unknown) graph $G$ to find a hidden goal node…
In this article we will present a graph partitioning algorithm which partitions a graph into two different types of components: the well-known `strongly connected components' as well as another type of components we call `connected acyclic…
Directed mixed graphs permit directed and bidirected edges between any two vertices. They were first considered in the path analysis developed by Sewall Wright and play an essential role in statistical modeling. We introduce a matrix…
In complex networks, especially social networks, networks could be divided into disjoint partitions that the ratio between the number of internal edges (the edges between the vertices within same partition) to the number of outer edges…
Graphs are nowadays ubiquitous in the fields of signal processing and machine learning. As a tool used to express relationships between objects, graphs can be deployed to various ends: I) clustering of vertices, II) semi-supervised…
Graphs naturally appear in several real-world contexts including social networks, the web network, and telecommunication networks. While the analysis and the understanding of graph structures have been a central area of study in algorithm…
In this work, for the given adjacency matrix of a graph, we present an algorithm which checks the connectivity of a graph and computes all of its connected components. Also, it is mathematically proved that the algorithm presents all the…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
Network (graph) data analysis is a popular research topic in statistics and machine learning. In application, one is frequently confronted with graph two-sample hypothesis testing where the goal is to test the difference between two graph…
We demonstrate that a graph-based search algorithm-relying on the construction of an approximate neighborhood graph-can directly work with challenging non-metric and/or non-symmetric distances without resorting to metric-space mapping…
Two fundamental algorithm-design paradigms are Tree Search and Dynamic Programming. The techniques used therein have been shown to complement one another when solving the complete set partitioning problem, also known as the coalition…
We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size…
This paper shows the weighted matching problem on general graphs can be solved in time $O(n(m + n\log n))$ for $n$ and $m$ the number of vertices and edges, respectively. This was previously known only for bipartite graphs. The crux is a…
Cut-based directed graph (digraph) clustering often focuses on finding dense within-cluster or sparse between-cluster connections, similar to cut-based undirected graph clustering methods. In contrast, for flow-based clusterings the edges…
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…
Many real networks are complex and have power-law vertex degree distribution, short diameter, and high clustering. We analyze the network model based on thresholding of the summed vertex weights, which belongs to the class of networks…