Related papers: Efficient Farthest-Point Queries in Two-Terminal S…
The distance of a graph from being triangle-free is a fundamental graph parameter, counting the number of edges that need to be removed from a graph in order for it to become triangle-free. Its corresponding computational problem is the…
Let $\mathcal{P}$ be the surface of a convex polyhedron with $n$ vertices. We consider the two-point shortest path query problem for $\mathcal{P}$: Constructing a data structure so that given any two query points $s$ and $t$ on…
Complex systems of interacting components often can be modeled by a simple graph $\mathcal{G}$ that consists of a set of $n$ nodes and a set of $m$ edges. Such a graph can be represented by an adjacency matrix $A\in\R^{n\times n}$, whose…
We study network design with a cost structure motivated by redundancy in data traffic. We are given a graph, g groups of terminals, and a universe of data packets. Each group of terminals desires a subset of the packets from its respective…
In this paper, we investigate some basic connectivity problems in directed graphs (digraphs). Let $G$ be a digraph with $m$ edges and $n$ vertices, and let $G\setminus e$ be the digraph obtained after deleting edge $e$ from $G$. As a first…
One of the most fundamental problems in large scale network analysis is to determine the importance of a particular node in a network. Betweenness centrality is the most widely used metric to measure the importance of a node in a network.…
Learning the latent network structure from large scale multivariate point process data is an important task in a wide range of scientific and business applications. For instance, we might wish to estimate the neuronal functional…
In the range closest pair problem, we want to construct a data structure storing a set $S$ of $n$ points in the plane, such that for any axes-parallel query rectangle $R$, the closest pair in the set $R \cap S$ can be reported. The…
We introduce a general framework for analyzing data modeled as parameterized families of networks. Building on a Gromov-Wasserstein variant of optimal transport, we define a family of parameterized Gromov-Wasserstein distances for comparing…
Connectivity query processing is a fundamental problem in graph processing. Given an undirected graph and two query vertices, the problem aims to identify whether they are connected via a path. Given frequent edge updates in real graph…
Redundancy needs more precise characterization as it is a major factor in the evolution and robustness of networks of multivariate interactions. We investigate the complexity of such interactions by inferring a connection transitivity that…
We study the 2-Disjoint Shortest Paths (2-DSP) problem: given a directed weighted graph and two terminal pairs $(s_1,t_1)$ and $(s_2,t_2)$, decide whether there exist vertex-disjoint shortest paths between each pair. Building on recent…
A majority of real life networks are weighted and sparse. The present article aims at characterization of weighted networks based on sparsity, as a measure of inherent diversity, of different network parameters. It utilizes sparsity index…
We study the problem of constructing a data structure that can store a two-dimensional polygonal curve $P$, such that for any query segment $\overline{ab}$ one can efficiently compute the Fr\'{e}chet distance between $P$ and…
We consider the problem of constructing a communication infrastructure from scratch, for a collection of identical wireless nodes. Combinatorially, this means a) finding a set of links that form a strongly connected spanning graph on a set…
The network unreliability problem asks for the probability that a given undirected graph gets disconnected when every edge independently fails with a given probability $p$. Valiant (1979) showed that this problem is \#P-hard; therefore, the…
We describe the structure of the graphs with the smallest average distance and the largest average clustering given their order and size. There is usually a unique graph with the largest average clustering, which at the same time has the…
We present a near linear time algorithm for constructing hierarchical nets in finite metric spaces with constant doubling dimension. This data-structure is then applied to obtain improved algorithms for the following problems: Approximate…
In large networks, using the length of shortest paths as the distance measure has shortcomings. A well-studied shortcoming is that extending it to disconnected graphs and directed graphs is controversial. The second shortcoming is that a…
In nearest-neighbor classification problems, a set of $d$-dimensional training points are given, each with a known classification, and are used to infer unknown classifications of other points by using the same classification as the nearest…