Abstract :
A hierarchical edge-weight network (HEWN) of solving the maximum clique problem was presented in Tang, P. and Huang, Z. (1998). With the help of HEWN, the maximum clique problem was solved in polynomial time Tang, P. and Huang, Z. (1998). In this paper, the HEWN algorithm was anatomized with starting from the storage structure of HEWN. In the anatomizing procedure, by compared with the maximum complete subgraph tree (MCST) algorithm, we point out that when 2j>n, the underlying exponential times of creating and modifying the guiding matrices (GMs) exists in the HEWN algorithm, and its time complexity is O(Cj 2j-n), where n is the number of the vertices in a graph and j is the size of the maximum clique in the graph
Keywords :
computational complexity; graph theory; matrix algebra; HEWN algorithm; complexity analysis; guiding matrices; hierarchical edge-weight network; maximum clique problem; maximum complete subgraph tree algorithm; polynomial time; time complexity; Algorithm design and analysis; Computer science; Electronic mail; Intelligent systems; Polynomials;
