An O(20.304n) Algorithm for Solving Maximum Independent Set Problem
IEEE Transactions on Computers
An optimal algorithm for finding a maximum independent set of a circular-arc graph
SIAM Journal on Computing
Polynomial algorithms for the maximum stable set problem on particular classes of P5-free graphs
Information Processing Letters
An O(m + nlog n) algorithm for the maximum-clique problem in circular-arc graphs
Journal of Algorithms
Finding maximum independent sets in sparse and general graphs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
What are the least tractable instances of max independent set?
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Permutation Graphs and Transitive Graphs
Journal of the ACM (JACM)
Algorithm 457: finding all cliques of an undirected graph
Communications of the ACM
Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, Workshop, October 11-13, 1993
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Measure and conquer: a simple O(20.288n) independent set algorithm
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
An Efficient Branch-and-bound Algorithm for Finding a Maximum Clique with Computational Experiments
Journal of Global Optimization
The worst-case time complexity for generating all maximal cliques and computational experiments
Theoretical Computer Science - Computing and combinatorics
An efficient branch-and-bound algorithm for finding a maximum clique
DMTCS'03 Proceedings of the 4th international conference on Discrete mathematics and theoretical computer science
Hi-index | 0.00 |
The maximum clique problem is known to be a typical NP-complete problem, and hence it is believed to be impossible to solve it in polynomial-time. So, it is important to know a reasonable sufficient condition under which the maximum clique problem can be proved to be polynomial-time solvable. In this paper, given a graph of n vertices and whose maximum degree is Δ, we prove that if Δ is less than or equal to 2.493dlg n (d≥1: a constant), then the maximum clique problem is solvable in the polynomial time of O(n2+d). The proof is based on a very simple algorithm which is obtained from an algorithm CLIQUES that generates all maximal cliques in a depth-first way in O(3n/3)-time (which is published in Theoretical Computer Science 363, 2006, as "The worstcase time complexity for generating all maximal cliques and computational experiments" by E. Tomita et al.). The proof itself is very simple.