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Random walk algorithms are crucial for sampling and approximation problems in statistical physics and theoretical computer science. The mixing property is necessary for Markov chains to approach stationary distributions and is facilitated…
We consider the problem of performing a random walk in a distributed network. Given bandwidth constraints, the goal of the problem is to minimize the number of rounds required to obtain a random walk sample. Das Sarma et al. [PODC'10] show…
We study the following problem: given an integer $k \ge 3$ and a simple graph $G$, sample a connected induced $k$-node subgraph of $G$ uniformly at random. This is a fundamental graph mining primitive with applications in social network…
We study quantum walks on general graphs from the point of view of scattering theory. For a general finite graph we choose two vertices and attach one half line to each. We are interested in walks that proceed from one half line, through…
Randomized algorithms for deciding satisfiability were shown to be effective in solving problems with thousands of variables. However, these algorithms are not complete. That is, they provide no guarantee that a satisfying assignment, if…
The quantum walk dynamics obey the laws of quantum mechanics with an extra locality constraint, which demands that the evolution operator is local in the sense that the walker must visit the neighboring locations before endeavoring to…
We present new, more efficient algorithms for estimating random walk scores such as Personalized PageRank from a given source node to one or several target nodes. These scores are useful for personalized search and recommendations on…
Node counting on a graph is subject to some fundamental theoretical limitations, yet a solution to such problems is necessary in many applications of graph theory to real-world systems, such as collective robotics and distributed sensor…
In this paper, we propose a deterministic algorithm that approximates the optimal path cover on weighted undirected graphs. Based on the 1/2-Approximation Path Cover Algorithm by Moran et al., we add a procedure to remove the redundant…
Using the growing volumes of vehicle trajectory data, it becomes increasingly possible to capture time-varying and uncertain travel costs in a road network, including travel time and fuel consumption. The current paradigm represents a road…
Analyzing the mixing time of random walks is a well-studied problem with applications in random sampling and more recently in graph partitioning. In this work, we present new analysis of random walks and evolving sets using more…
A random walk is a basic stochastic process on graphs and a key primitive in the design of distributed algorithms. One of the most important features of random walks is that, under mild conditions, they converge to a stationary distribution…
Message-passing architectures struggle to sufficiently model long-range dependencies in node and graph prediction tasks. We propose a novel approach exploiting hierarchical graph structures and adaptive random walks to address this…
Finding large or heavy matchings in graphs is a ubiquitous combinatorial optimization problem. In this paper, we engineer the first non-trivial implementations for approximating the dynamic weighted matching problem. Our first algorithm is…
In this paper, we revisit the problem of classical \textit{meeting times} of random walks in graphs. In the process that two tokens (called agents) perform random walks on an undirected graph, the meeting times are defined as the expected…
Random Walk is a basic algorithm to explore the structure of networks, which can be used in many tasks, such as local community detection and network embedding. Existing random walk methods are based on single networks that contain limited…
In this note, we try to analyze and clarify the intriguing interplay between some counting problems related to specific thermalized weighted graphs and random walks consistent with such graphs.
Continuous-time quantum walks have proven to be an extremely useful framework for the design of several quantum algorithms. Often, the running time of quantum algorithms in this framework is characterized by the quantum hitting time: the…
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…
It is a fact simple to establish that the mixing time of the simple random walk on a d-regular graph $G_n$ with n vertices is asymptotically bounded from below by $d/ ((d-2)\log (d-1))\log n$. Such a bound is obtained by comparing the walk…