Article
Version 1
This version is not peer-reviewed
Probabilistic Cellular Automata Monte Carlo for the Maximum Clique Problem
Version 1
: Received: 30 August 2024 / Approved: 30 August 2024 / Online: 30 August 2024 (14:56:57 CEST)
How to cite: Troiani, A. Probabilistic Cellular Automata Monte Carlo for the Maximum Clique Problem. Preprints 2024, 2024082259. https://doi.org/10.20944/preprints202408.2259.v1 Troiani, A. Probabilistic Cellular Automata Monte Carlo for the Maximum Clique Problem. Preprints 2024, 2024082259. https://doi.org/10.20944/preprints202408.2259.v1
Abstract
We consider the problem of finding the largest clique of a graph. This is an NP-hard problem and no exact algorithm to solve it exactly in polynomial time is known to exist.
Several heuristic approaches have been proposed to find approximate solutions, Markov Chain Monte Carlo being one of those. In the context of Markov Chain Monte Carlo, we present a class of ``parallel dynamics'', known as Probabilistic Cellular Automata, which can be used in place of the more standard choice of sequential ``single spin flip'' to sample from a probability distribution concentrated on the largest cliques of the graph. We perform a numerical comparison between the two classes of chains both in terms of the quality of the solution and in terms of computational time. We show that the parallel dynamics are considerably faster than the sequential one while providing solutions of comparable quality.
Keywords
Maximum Clique Problem; Probabilistic Cellular Automata; Monte Carlo Markov Chain; QUBO; Parallel Computing
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment