scholarly journals Graphs and Matroids Weighted in a Bounded Incline Algebra

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Ling-Xia Lu ◽  
Bei Zhang
Keyword(s):  
Shortest Path ◽  
Independent Set ◽  
Shortest Path Problem ◽  
Maximum Independent Set ◽  
Independent Set Problem ◽  
Uniform Approach ◽  
Longest Path ◽  
Longest Path Problem ◽  
Maximum Independent Set Problem ◽  
Reliable Path

Firstly, for a graph weighted in a bounded incline algebra (or called a dioid), a longest path problem (LPP, for short) is presented, which can be considered the uniform approach to the famous shortest path problem, the widest path problem, and the most reliable path problem. The solutions for LPP and related algorithms are given. Secondly, for a matroid weighted in a linear matroid, the maximum independent set problem is studied.

Parallel Solution for Maximum Independent Set Problem by Programmable Tile Assembly

2016 ◽  
Vol 25 (2) ◽  
pp. 203-208 ◽  
Author(s):  
Yufang Huang ◽  
Jianhua Xiao ◽  
Keqin Jiang ◽  
Zhihua Chen
Keyword(s):  
Independent Set ◽  
Maximum Independent Set ◽  
Independent Set Problem ◽  
Parallel Solution ◽  
Tile Assembly ◽  
Maximum Independent Set Problem

Fuzzy Maximum Independent Set Problem

2014 ◽  
Vol 687-691 ◽  
pp. 1161-1165
Author(s):  
Dong Ling Luo ◽  
Chen Yin Wang ◽  
Yang Yi ◽  
Dong Ling Zhang ◽  
Xiao Cong Zhou
Keyword(s):  
Dominating Set ◽  
Fuzzy Variable ◽  
Independent Set ◽  
Credibility Theory ◽  
Covering Problem ◽  
Maximum Independent Set ◽  
Independent Set Problem ◽  
Intelligence Algorithm ◽  
Hybrid Intelligence ◽  
Maximum Independent Set Problem

Edge covering problem, dominating set problem, and independent set problem are classic problems in graph theory except for vertex covering problem. In this paper, we study the maximum independent set problem under fuzzy uncertainty environments, which aims to search for the independent set with maximum value in a graph. First, credibility theory is introduced to describe the fuzzy variable. Three decision models are performed based on the credibility theory. A hybrid intelligence algorithm which integrates genetic algorithm and fuzzy simulation is proposed due to the unavailability of traditional algorithm. Finally, numerical experiments are performed to prove the efficiency of the fuzzy decision modes and the hybrid intelligence algorithm.

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