Approximation Algorithms for Hamming Clustering Problems

We study Hamming versions of two classical clustering problems. The Hamming radius p-clustering problem (HRC) for a set S of k binary strings, each of length n, is to find p binary strings of length n that minimize the maximum Hamming distance between a string in S and the closest of the p strings; this minimum value is termed the p-radius of S and is denoted by . The related Hamming diameter p-clustering problem (HDC) is to split S into p groups so that the maximum of the Hamming group diameters is minimized; this latter value is called the p-diameter of S. We provide an integer programming formulation of HRC which yields exact solutions in polynomial time whenever k is constant. We also observe that HDC admits straightforward polynomial-time solutions when k = O(logn) and p = O(1), or when p = 2. Next, by reduction from the corresponding geometric p-clustering problems in the plane under the L1 metric, we show that neither HRC nor HDC can be approximated within any constant factor ...

• Type: Conference
• Year: 2000
• Where: CPM
• Authors: Leszek Gasieniec, Jesper Jansson, Andrzej Lingas
• Keywords: Combinatorics, CPM 2000, Hamming, Hamming Diameter, P-clustering Problems