On the tractability of the maximum clique problem
R. Dharmarajan, and D. Ramachandran
TL;DR
This paper explores the theoretical possibility of a polynomial-time algorithm for the NP-complete maximum clique problem, providing a pseudo-code outline and analysis of its correctness and efficiency.
Contribution
It presents a partially non-constructive proof of the existence of an exact polynomial-time algorithm for the maximum clique problem.
Findings
Proof of existence of a polynomial-time algorithm
Pseudo-code outline of the proposed algorithm
Analysis confirming the algorithm's correctness and efficiency
Abstract
The maximum clique problem is a classical NP-complete problem in graph theory and has important applications in many domains. In this paper we show, in a partially non-constructive way, the existence of an exact polynomial-time algorithm for this problem. We outline the algorithm in pseudo-code style. Then we prove its exactness and efficiency by analysis.
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Taxonomy
TopicsAdvanced Optimization Algorithms Research · Matrix Theory and Algorithms · Algebraic and Geometric Analysis