Related papers: Sampling Directed Eulerian Tours in $\widetilde O(…
Randomising networks using a naive `accept-all' edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities for…
Efficient techniques to navigate networks with local information are fundamental to sample large-scale online social systems and to retrieve resources in peer-to-peer systems. Biased random walks, i.e. walks whose motion is biased on…
We give an algorithm that takes a directed graph $G$ undergoing $m$ edge insertions with lengths in $[1, W]$, and maintains $(1+\epsilon)$-approximate shortest path distances from a fixed source $s$ to all other vertices. The algorithm is…
Motivation: The Mapper algorithm is an essential tool to explore shape of data in topology data analysis. With a dataset as an input, the Mapper algorithm outputs a graph representing the topological features of the whole dataset. This…
We consider the directed minimum weight cycle problem in the fully dynamic setting. To the best of our knowledge, so far no fully dynamic algorithms have been designed specifically for the minimum weight cycle problem in general digraphs.…
Motivated by the recent result of [EJT10] showing that MSO properties are Logspace computable on graphs of bounded tree-width, we consider the complexity of computing the determinant of the adjacency matrix of a bounded tree-width graph and…
We give new partially-dynamic algorithms for the all-pairs shortest paths problem in weighted directed graphs. Most importantly, we give a new deterministic incremental algorithm for the problem that handles updates in…
The random order graph streaming model has received significant attention recently, with problems such as matching size estimation, component counting, and the evaluation of bounded degree constant query testable properties shown to admit…
An Eulerian walk (or Eulerian trail) is a walk (resp. trail) that visits every edge of a graph $G$ at least (resp. exactly) once. This notion was first discussed by Leonhard Euler while solving the famous Seven Bridges of K\"{o}nigsberg…
A new efficient algorithm is presented for finding all simple cycles that satisfy a length constraint in a directed graph. When the number of vertices is non-trivial, most cycle-finding problems are of practical interest for sparse graphs…
We introduce a non-equilibrium discrete-time random walk model on multiplex networks, in which at each time step the walker first undergoes a random jump between neighboring nodes in the same layer, and then tries to hop from one node to…
Given a traversal algorithm, cover time is the expected number of steps needed to visit all nodes in a given graph. A smaller cover time means a higher exploration efficiency of traversal algorithm. Although random walk algorithms have been…
We consider approximations for computing minimum weighted cuts in directed graphs. We consider both rooted and global minimum cuts, and both edge-cuts and vertex-cuts. For these problems we give randomized Monte Carlo algorithms that…
Random walk based distributed algorithms make use of a token that circulates in the system according to a random walk scheme to achieve their goal. To study their efficiency and compare it to one of the deterministic solutions, one is led…
This paper presents the first discrete-time distributed algorithm to track the tightest ellipsoids that outer approximates the global dynamic intersection of ellipsoids. Given an undirected network, we consider a setup where each node…
We show new applications of the nearest-neighbor chain algorithm, a technique that originated in agglomerative hierarchical clustering. We apply it to a diverse class of geometric problems: we construct the greedy multi-fragment tour for…
In this paper we present a simple but powerful subgraph sampling primitive that is applicable in a variety of computational models including dynamic graph streams (where the input graph is defined by a sequence of edge/hyperedge insertions…
By a theorem of Volkov (2001) we know that on most graphs with positive probability the linearly vertex-reinforced random walk (VRRW) stays within a finite "trapping" subgraph at all large times. The question of whether this tail behavior…
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…
Let $G=(V,E)$ be an unweighted undirected graph with $n$ vertices and $m$ edges. Let $g$ be the girth of $G$, that is, the length of a shortest cycle in $G$. We present a randomized algorithm with a running time of $\tilde{O}\big(\ell \cdot…