Related papers: Theoretically and Practically Efficient Resistance…
Previous work has shown the effectiveness of random walk hitting times as a measure of dissimilarity in a variety of graph-based learning problems such as collaborative filtering, query suggestion or finding paraphrases. However,…
We study the problem of computing isochrones in road networks, where the objective is to identify the region that is reachable from a given source within a certain amount of time. While there is a wide range of practical applications for…
In this paper we study the problem of maintaining the strongly connected components of a graph in the presence of failures. In particular, we show that given a directed graph $G=(V,E)$ with $n=|V|$ and $m=|E|$, and an integer value $k\geq…
We study the design of robust subexponential algorithms for classical connectivity problems on intersection graphs of similarly sized fat objects in $\mathbb{R}^d$. In this setting, each vertex corresponds to a geometric object, and two…
Let $G=(V,E)$ be a finite, combinatorial graph. We define a notion of curvature on the vertices $V$ via the inverse of the resistance distance matrix. We prove that this notion of curvature has a number of desirable properties. Graphs with…
The All-Pairs Shortest Paths (APSP) problem is one of the fundamental problems in theoretical computer science. It asks to compute the distance matrix of a given $n$-vertex graph. We revisit the classical problem of maintaining the distance…
Querying graph data with low latency is an important requirement in application domains such as social networks and knowledge graphs. Graph queries perform multiple hops between vertices. When data is partitioned and stored across multiple…
We investigate searching efficiency of different kinds of random walk on complex networks which rely on local information and one-step memory. For the studied navigation strategies we obtained theoretical and numerical values for the graph…
Digital presence in the world of online social media entails significant privacy risks. In this work we consider a privacy threat to a social network in which an attacker has access to a subset of random walk-based node similarities, such…
Given a time-evolving graph, how can we track similarity between nodes in a fast and accurate way, with theoretical guarantees on the convergence and the error? Random Walk with Restart (RWR) is a popular measure to estimate the similarity…
Mutually connected components (MCCs) play an important role as a measure of resilience in the study of interdependent networks. Despite their importance, an efficient algorithm to obtain the statistics of all MCCs during the removal of…
We describe a new forward-backward variant of Dijkstra's and Spira's Single-Source Shortest Paths (SSSP) algorithms. While essentially all SSSP algorithm only scan edges forward, the new algorithm scans some edges backward. The new…
To quantify the fundamental evolution of time-varying networks, and detect abnormal behavior, one needs a notion of temporal difference that captures significant organizational changes between two successive instants. In this work, we…
In the model of \emph{local computation algorithms} (LCAs), we aim to compute the queried part of the output by examining only a small (sublinear) portion of the input. Many recently developed LCAs on graph problems achieve time and space…
Let $G$ be a connected graph with $V(G)=\{1,\dotsc,n\}$. Then the resistance distance between any two vertices $i$ and $j$ is given by $r_{ij}:=l_{ii}^{\dag} + l_{jj}^{\dag}-2 l_{ij}^{\dag}$, where $l_{ij}^\dag$ is the $(i,j)^{\rm th}$…
We study the problem of efficiently approximating the \textit{effective resistance} (ER) on undirected graphs, where ER is a widely used node proximity measure with applications in graph spectral sparsification, multi-class graph…
The Lanczos algorithm has proven itself to be a valuable matrix eigensolver for problems with large dimensions, up to hundreds of millions or even tens of billions. The computational cost of using any Lanczos algorithm is dominated by the…
We present a novel algorithm for dynamic routing with dedicated path protection which, as the presented simulation results suggest, can be efficient and exact. We present the algorithm in the setting of optical networks, but it should be…
Motion-planning problems, such as manipulation in cluttered environments, often require a collision-free shortest path to be computed quickly given a roadmap graph. Typically, the computational cost of evaluating whether an edge of the…
Transportation cost is an attractive similarity measure between probability distributions due to its many useful theoretical properties. However, solving optimal transport exactly can be prohibitively expensive. Therefore, there has been…