Related papers: Theoretically and Practically Efficient Resistance…
We study the Lanczos algorithm where the initial vector is sampled uniformly from $\mathbb{S}^{n-1}$. Let $A$ be an $n \times n$ Hermitian matrix. We show that when run for few iterations, the output of Lanczos on $A$ is almost…
We define and study two new kinds of "effective resistances" based on hubs-biased -- hubs-repelling and hubs-attracting -- models of navigating a graph/network. We prove that these effective resistances are squared Euclidean distances…
Resistance distance computation is a fundamental problem in graph analysis, yet existing random walk-based methods are limited to approximate solutions and suffer from poor efficiency on small-treewidth graphs (e.g., road networks). In…
In this paper we give a survey of methods used to calculate values of resistance distance (also known as effective resistance) in graphs. Resistance distance has played a prominent role not only in circuit theory and chemistry, but also in…
This article discusses a geometric perspective on the well-known fact in graph theory that the effective resistance is a metric on the nodes of a graph. The classical proofs of this fact make use of ideas from electrical circuits or random…
Partitioning a graph into three pieces, with two of them large and connected, and the third a small ``separator'' set, is useful for improving the performance of a number of combinatorial algorithms. This is done using the second…
We investigate the concept of effective resistance in connection graphs, expanding its traditional application from undirected graphs. We propose a robust definition of effective resistance in connection graphs by focusing on the duality of…
Recent work in theoretical computer science and scientific computing has focused on nearly-linear-time algorithms for solving systems of linear equations. While introducing several novel theoretical perspectives, this work has yet to lead…
Graph curvature provides geometric priors for Graph Neural Networks (GNNs), enhancing their ability to model complex graph structures, particularly in terms of structural awareness, robustness, and theoretical interpretability. Among…
We consider the fundamental problems of determining the rooted and global edge and vertex connectivities (and computing the corresponding cuts) in directed graphs. For rooted (and hence also global) edge connectivity with small integer…
Researchers have designed many algorithms to measure the distances between graph nodes, such as average hitting times of random walks, cosine distances from DeepWalk, personalized PageRank, etc. Successful although these algorithms are,…
We present an algorithm for optimal guidance of users in road networks. It is a "stochastic-on-time-arrival (SOTA)"-like algorithm which calculates optimal guidance strategies with reliable paths, for road network origin-destination pairs.…
Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that…
Lanczos-type algorithms are efficient and easy to implement. Unfortunately they breakdown frequently and well before convergence has been achieved. These algorithms are typically based on recurrence relations which involve formal orthogonal…
In network theory, the concept of effective resistance is a distance measure on a graph that relates the global network properties to individual connections between nodes. In addition, the Kron reduction method is a standard tool for…
This work introduces a method for determining the energy spectrum of lattice quantum chromodynamics (LQCD) by applying the Lanczos algorithm to the transfer matrix and using a bootstrap generalization of the Cullum-Willoughby method to…
Given an input $x$, and a search problem $F$, local computation algorithms (LCAs) implement access to specified locations of $y$ in a legal output $y \in F(x)$, using polylogarithmic time and space. Mansour et al., (2012), had previously…
This paper presents an introduction and expository account of a beautiful, current, and active application of recursions to the computation of resistance distance. Resistance distance, also referred to as effective resistance, is a…
In this paper, we study the problem of map matching with travel time constraints. Given a sequence of $k$ spatio-temporal measurements and an embedded path graph with travel time costs, the goal is to snap each measurement to a close-by…
The Lanczos method is one of the most powerful and fundamental techniques for solving an extremal symmetric eigenvalue problem. Convergence-based error estimates depend heavily on the eigenvalue gap. In practice, this gap is often…