Title :
A polynomial-time algorithm for the maximum clique problem
Author :
Akbari, Zohreh O.
Author_Institution :
Dept. of Math. & Comput. Sci., Friedrich Schiller Univ., Jena, Germany
Abstract :
After more than six decades of its introduction, the maximum clique problem, which is one of the most applicable problems in the graph theory, has still no polynomial-time solution. This paper presents a polynomial-time algorithm for this problem, which detects the maximum clique of a given graph through a recursive approach. This polynomial solution to the clique problem, as an NP-complete problem, causes every problem in NP to have a polynomial solution, which leads to the equality of P and NP complexity classes.
Keywords :
computational complexity; graph theory; NP complexity class; NP-complete problem; P complexity class; graph theory; maximum clique problem; polynomial solution; polynomial-time algorithm; recursive approach; Approximation algorithms; Approximation methods; NP-complete problem; Optimization; Polynomials; Time complexity; Computational Complexity Theory; Maximum Clique Problem; NP-Complete Problems; P versus NP Problem; Polynomial-Time Algorit hm; Recursive Opti mization;
Conference_Titel :
Computer and Information Science (ICIS), 2013 IEEE/ACIS 12th International Conference on
Conference_Location :
Niigata
DOI :
10.1109/ICIS.2013.6607889
