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Nearly Linear Time Algorithm for Mean Hitting Times of Random Walks on a Graph

Published: 22 January 2020 Publication History

Abstract

For random walks on a graph, the mean hitting time $H_j$ from a vertex i chosen from the stationary distribution to the target vertex j can be used as a measure of importance for vertex j, while the Kemeny constant K is the mean hitting time from a vertex i to a vertex j selected randomly according to the stationary distribution. Both quantities have found a large variety of applications in different areas. However, their high computational complexity limits their applications, especially for large networks with millions of vertices. In this paper, we first establish a connection between the two quantities, representing K in terms of $H_j$ for all vertices. We then express both quantities in terms of quadratic forms of the pseudoinverse for graph Laplacian, based on which we develop an efficient algorithm that provides an approximation of $H_j$ for all vertices and K in nearly linear time with respect to the edge number, with high probability. Extensive experiment results on real-life and model networks validate both the efficiency and accuracy of the proposed algorithm.

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  • (2024)Means of Hitting Times for Random Walks on Graphs: Connections, Computation, and OptimizationACM Transactions on Knowledge Discovery from Data10.1145/370856119:2(1-35)Online publication date: 17-Dec-2024
  • (2024)Efficient Approximation of Kemeny's Constant for Large GraphsProceedings of the ACM on Management of Data10.1145/36549372:3(1-26)Online publication date: 30-May-2024
  • (2024)Fast Computation of Kemeny's Constant for Directed GraphsProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3637528.3671859(3472-3483)Online publication date: 25-Aug-2024
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cover image ACM Conferences
WSDM '20: Proceedings of the 13th International Conference on Web Search and Data Mining
January 2020
950 pages
ISBN:9781450368223
DOI:10.1145/3336191
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 22 January 2020

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Author Tags

  1. complex network
  2. hitting time
  3. kemeny constant
  4. node centrality
  5. random walk
  6. spectral algorithm

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  • Research-article

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  • the National Natural Science Foundation of China
  • the National Key R & D Program of China

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WSDM '20

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Overall Acceptance Rate 498 of 2,863 submissions, 17%

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Cited By

View all
  • (2024)Means of Hitting Times for Random Walks on Graphs: Connections, Computation, and OptimizationACM Transactions on Knowledge Discovery from Data10.1145/370856119:2(1-35)Online publication date: 17-Dec-2024
  • (2024)Efficient Approximation of Kemeny's Constant for Large GraphsProceedings of the ACM on Management of Data10.1145/36549372:3(1-26)Online publication date: 30-May-2024
  • (2024)Fast Computation of Kemeny's Constant for Directed GraphsProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3637528.3671859(3472-3483)Online publication date: 25-Aug-2024
  • (2024)Resistance Distances in Directed Graphs: Definitions, Properties, and ApplicationsTheoretical Computer Science10.1016/j.tcs.2024.114700(114700)Online publication date: Jun-2024
  • (2023)Measures and Optimization for Robustness and Vulnerability in Disconnected NetworksIEEE Transactions on Information Forensics and Security10.1109/TIFS.2023.327997918(3350-3362)Online publication date: 2023
  • (2023)Hitting Times of Random Walks on Edge Corona Product GraphsThe Computer Journal10.1093/comjnl/bxac189Online publication date: 9-Jan-2023
  • (2021)An Efficient and Scalable Algorithm for Estimating Kemeny's Constant of a Markov Chain on Large GraphsProceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining10.1145/3447548.3467431(964-974)Online publication date: 14-Aug-2021

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