Poising on Ariadne's thread: An algorithm for computing a maximum clique in polynomial time
Ioannis Avramopoulos
TL;DR
This paper introduces a polynomial-time algorithm for the maximum clique problem, using a continuous game-theoretic approach and a dynamical system, claiming to imply P = NP.
Contribution
It presents a novel polynomial-time algorithm for maximum clique, based on a continuous game-theoretic model and a parameter-dependent dynamical system.
Findings
Algorithm converges to a maximum clique when parameter matches maximum clique size
Proposes a new approach linking game theory and combinatorial optimization
Claims to imply P = NP
Abstract
In this paper, we present a polynomial-time algorithm for the maximum clique problem, which implies P = NP. Our algorithm is based on a continuous game-theoretic representation of this problem and at its heart lies a discrete-time dynamical system. The rule of our dynamical system depends on a parameter such that if this parameter is equal to the maximum-clique size, the iterates of our dynamical system are guaranteed to converge to a maximum clique.
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Advanced Graph Theory Research · Machine Learning and Algorithms