The Complexity and Improved Heuristic Algorithms for Binary Fingerprints Clustering
Peiqiang Liu, Daming Zhu, Xie Qing-song, Fan Hui, Ma Shaohan · 2008
Abstract: Binary fingerprints clustering is used in the classification analysis of gene expression data. It has important values in disease diagnosis. In this paper, we prove the binary fingerprints clustering problem for 2 missing values per fingerprint to be NP-Hard, and improve the Figueroa’s heuristic algorithm. The new algorithm improves the implementation method for the original algorithm. Firstly, we use the chained table to store the sets of compatible vertices. The chained tables can be produced by scanning the fingerprint vectors bit by bit. Thus the time complexity for producing the sets of compatible vertices is reduced from O(m•n•2 p) to O(m•(n−p+1)•2 p). And the the running time of finding a unique maximal clique or a maximal clique is improved from O(m•p•2 p) to O(m•2 p). The real testing displays that the improved algorithm takes 49 % or less space complexity of the original algorithm averagely for the computation of the same instance. It can use 20 % time of the original algorithm for solving the same instance. Particularly, the new algorithm can almost always use not more than 11 % time of the original algorithm to solve the instance with more than 6 missing values per fingerprint.