Probe Machine Based Computing Model for Maximum Clique Problem

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.