Complexity and Improved Heuristic Algorithms for Binary Fingerprints Clustering
两元指纹向量聚类问题的复杂性与改进启发式算法

This paper proves the binary fingerprints clustering problem for 2 missing values per fingerprint is NP-Hard, and improves the Figueroa's heuristic algorithm. The new algorithm improves the implementation method for the original algorithm. Firstly, the linked list is used to store the sets of compatible vertices. The linked list 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·2p) to O(m·(n-p+1)·2p), and the the running time of finding a unique maximal clique or a maximal clique is improved from O(m·p·2p) to O(m·2p). The real testing displays that the improved algorithm takes 49% or lower space complexity of the original algorithm on the average 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.