research-article

Fast Connectivity Minimization on Large-Scale Networks

Authors:

Hanghang TongAuthors Info & Claims

ACM Transactions on Knowledge Discovery from Data (TKDD), Volume 15, Issue 3

Article No.: 53, Pages 1 - 25

https://doi.org/10.1145/3442342

Published: 03 May 2021 Publication History

Abstract

The connectivity of networks has been widely studied in many high-impact applications, ranging from immunization, critical infrastructure analysis, social network mining, to bioinformatic system studies. Regardless of the end application domains, connectivity minimization has always been a fundamental task to effectively control the functioning of the underlying system. The combinatorial nature of the connectivity minimization problem imposes an exponential computational complexity to find the optimal solution, which is intractable in large systems. To tackle the computational barrier, greedy algorithm is extensively used to ensure a near-optimal solution by exploiting the diminishing returns property of the problem. Despite the empirical success, the theoretical and algorithmic challenges of the problems still remain wide open. On the theoretical side, the intrinsic hardness and the approximability of the general connectivity minimization problem are still unknown except for a few special cases. On the algorithmic side, existing algorithms are hard to balance between the optimization quality and computational efficiency. In this article, we address the two challenges by (1) proving that the general connectivity minimization problem is NP-hard and

is the best approximation ratio for any polynomial algorithms, and (2) proposing the algorithm CONTAIN and its variant CONTAIN+ that can well balance optimization effectiveness and computational efficiency for eigen-function based connectivity minimization problems in large networks.

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Cited By

Zhou XSun HLi WZhang Z(2024)Optimization on the smallest eigenvalue of grounded Laplacian matrix via edge additionTheoretical Computer Science10.1016/j.tcs.2023.114220980:COnline publication date: 1-Feb-2024
https://dl.acm.org/doi/10.1016/j.tcs.2023.114220
Ren RShao JBishop AZheng W(2023)Modeling and Detecting Communities in Node Attributed NetworksIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2022.319761235:7(7206-7219)Online publication date: 1-Jul-2023
https://dl.acm.org/doi/10.1109/TKDE.2022.3197612
Zhu LBao QZhang Z(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: 1-Jan-2023
https://dl.acm.org/doi/10.1109/TIFS.2023.3279979
Show More Cited By

Index Terms

Fast Connectivity Minimization on Large-Scale Networks
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Paths and connectivity problems

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Published In

cover image ACM Transactions on Knowledge Discovery from Data

ACM Transactions on Knowledge Discovery from Data Volume 15, Issue 3

June 2021

533 pages

ISSN:1556-4681

EISSN:1556-472X

DOI:10.1145/3454120

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Copyright © 2021 Association for Computing Machinery.

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Publication History

Published: 03 May 2021

Accepted: 01 December 2020

Revised: 01 August 2020

Received: 01 December 2019

Published in TKDD Volume 15, Issue 3

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NSF Program on Fairness in AI in collaboration with Amazon

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Cited By

Zhou XSun HLi WZhang Z(2024)Optimization on the smallest eigenvalue of grounded Laplacian matrix via edge additionTheoretical Computer Science10.1016/j.tcs.2023.114220980:COnline publication date: 1-Feb-2024
https://dl.acm.org/doi/10.1016/j.tcs.2023.114220
Ren RShao JBishop AZheng W(2023)Modeling and Detecting Communities in Node Attributed NetworksIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2022.319761235:7(7206-7219)Online publication date: 1-Jul-2023
https://dl.acm.org/doi/10.1109/TKDE.2022.3197612
Zhu LBao QZhang Z(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: 1-Jan-2023
https://dl.acm.org/doi/10.1109/TIFS.2023.3279979
Adiga APalmer NBaek YMortveit HRavi S(2022)Network Models and Simulation Analytics for Multi-scale Dynamics of Biological InvasionsFrontiers in Big Data10.3389/fdata.2022.7968975Online publication date: 7-Feb-2022
https://doi.org/10.3389/fdata.2022.796897

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