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  • Finding Nontrivial Minimum Fixed Points in Discrete Dynamical Systems: Complexity, Special Case Algorithms and Heuristics
Title: Finding Nontrivial Minimum Fixed Points in Discrete Dynamical Systems: Complexity, Special Case Algorithms and Heuristics
Networked discrete dynamical systems are often used to model the spread of contagions and decision-making by agents in coordination games. Fixed points of such dynamical systems represent configurations to which the system converges. In the dissemination of undesirable contagions (such as rumors and misinformation), convergence to fixed points with a small number of affected nodes is a desirable goal. Motivated by such considerations, we formulate a novel optimization problem of finding a nontrivial fixed point of the system with the minimum number of affected nodes. We establish that, unless P = NP, there is no polynomial-time algorithm for approximating a solution to this problem to within the factor n^(1 - epsilon) for any constant epsilon > 0. To cope with this computational intractability, we identify several special cases for which the problem can be solved efficiently. Further, we introduce an integer linear program to address the problem for networks of reasonable sizes. For solving the problem on larger networks, we propose a general heuristic framework along with greedy selection methods. Extensive experimental results on real-world networks demonstrate the effectiveness of the proposed heuristics. A full version of the manuscript, source code and data areavailable at: https://github.com/bridgelessqiu/NMIN-FPE  more » « less
Award ID(s):
1916805 1918656
NSF-PAR ID:
10376926
Author(s) / Creator(s):
; ; ; ; ; ;
Date Published:
Journal Name:
Proceedings of the AAAI Conference on Artificial Intelligence
Volume:
36
Issue:
9
ISSN:
2159-5399
Page Range / eLocation ID:
9422 to 9430
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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