(Peer-Reviewed) Probe Machine Based Computing Model for Maximum Clique Problem
CUI Jianzhong 崔建中 ¹ ⁴, YIN Zhixiang 殷志祥 ², TANG Zhen 唐震 ³, YANG Jing 杨静 ³
¹ Department of Computer, Huainan Union University, Huainan 232038, China
中国 淮南 淮南联合大学计算机系
² School of Mathematics, Physics and Statistics, Shanghai University Of Engineering Science, Shanghai 201620, China
中国 上海 上海工程技术大学 数理与统计学院
³ School of Mathematics and Big Data, AnHui University of Science & Technology, Huainan 232001, China
中国 淮南 安徽理工大学 数学与大数据学院
⁴ School of Electronic and Information Engineering, AnHui University Of Science & Technology, Huainan 232001, China
中国 淮南 安徽理工大学 电气与信息工程学院
Abstract
Probe Machine (PM) is a recently reported mathematic model with massive parallelism. Herein, we presented searching the maximum clique of an undirected graph with six vertices. We constructed data library containing n sublibraries, each sublibrary corresponded to a vertex in the given graph. Then, probe library according to the induced subgraph was designed in order to search and generate all maximal cliques. Subsequently, we performed probe operation, and all maximal cliques were generated in parallel.
The advantages of the proposed model lie in two aspects. On one hand, solution to NP-complete problem is generated in just one step of probe operation rather than found in vast solution space. On the other hand, the proposed model is highly parallel. The work demonstrates that PM is superior to TM in terms of searching capacity when tackling NP-complete problem.
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