A 16-competitive algorithm for hierarchical median problem

The hierarchical median problem consists of finding a hierarchical assignment function sequence of solutions to the well-known k-median problems with growing carclinality. This sequence is said to be r-competitive if the cost of each solution is at most r times of the optimum cost of median problem with a same cardinality, where r is called the competitive ratio. Previously the best algorithm available for this problem has competitive ratio 20.71. In this paper an improved algorithm is proposed with competitive ratio factor 16.