Algorithms for a maximum clique and a maximum independent set of a circle graph

Networks ◽  
1973 ◽  
Vol 3 (3) ◽  
pp. 261-273 ◽  
Author(s):  
F. Gavril
Keyword(s):  
Maximum Clique ◽  
Independent Set ◽  
Maximum Independent Set ◽  
Circle Graph

Parallel algorithms for finding a near-maximum independent set of a circle graph

1990 ◽  
Vol 1 (3) ◽  
pp. 263-267 ◽  
Author(s):  
Y. Takefuji ◽  
L.-L. Chen ◽  
K.-C. Lee ◽  
J. Huffman
Keyword(s):  
Parallel Algorithms ◽  
Independent Set ◽  
Maximum Independent Set ◽  
Circle Graph

scholarly journals Latest Algorithms on Particular Graph Classes

2020 ◽  
pp. 21-35
Author(s):  
Phan Thuan DO ◽  
Ba Thai PHAM ◽  
Viet Cuong THAN
Keyword(s):  
Optimization Problems ◽  
Linear Time ◽  
Maximum Clique ◽  
Independent Set ◽  
Maximum Independent Set ◽  
Np Hard ◽  
Induced Matching ◽  
Graph Classes ◽  
Maximum Induced Matching ◽  
Circular Arc Graphs

Many optimization problems such as Maximum Independent Set, Maximum Clique, Minimum Clique Cover and Maximum Induced Matching are NP-hard on general graphs. However, they could be solved in polynomial time when restricted to some particular graph classes such as comparability and co-comparability graph classes. In this paper, we summarize the latest algorithms solving some classical NP-hard problems on some graph classes over the years. Moreover, we apply the -redundant technique to obtain linear time O(j j) algorithms which find a Maximum Induced Matching on interval and circular-arc graphs. Inspired of these results, we have proposed some competitive programming problems for some programming contests in Vietnam in recent years.

Surface- Based Computing Model of Maximum Independent Set Problem

2011 ◽  
Vol 328-330 ◽  
pp. 1729-1733
Author(s):  
Yan Yang ◽  
Zhi Xiang Yin
Keyword(s):  
Polynomial Time ◽  
Maximum Clique ◽  
Independent Set ◽  
Maximum Independent Set ◽  
Complex Class ◽  
Independent Set Problem ◽  
Complete Problem ◽  
Computing Model ◽  
Np Complete ◽  
Maximum Independent Set Problem

About thirty years ago, the concept of the complexity of the problem was proposed. The most important complex class is P and NP class. Fruitful results of this concept are the existence of the so-called complex class complete problem. If the other issues of this class once solved in polynomial time, then the problem must exist polynomial time algorithms. Therefore, the complete problem is most difficult to solve, but because of their presence, we can choose any of them improved algorithm for a problem, so this kind of problem to get a good solution. DNA computing is a novel method that solving a class of intractable computational problems, in which the computing speeds up exponentially with the problem size. Up to now, many accomplishments have been made to improve its performance and increase its reliability. Maximum Independent Set problem (MIS) is a well-known NP-complete problem. Maximum Clique and Minimum Vertex Covering problem is equivalent to Maximum Independent Set problem. In this paper, we explore solving Maximum Independent Set problem by transforming it into equivalent 0-1 programming problem, and utilizing the surface computing model of that. The proposed method demonstrates universal nature of NP-complete problem.

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