Poising on Ariadne's thread: An algorithm for computing a maximum clique in polynomial time
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2020
- DOI:
- 10.48550/arXiv.2008.06167
- arXiv:
- arXiv:2008.06167
- Bibcode:
- 2020arXiv200806167A
- Keywords:
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- Computer Science - Computer Science and Game Theory;
- Computer Science - Computational Complexity