Simple algorithm for partial quantum search

Quite often in database search, we only, need to extract portion of the information about the satisfying item. We consider this problem in the following form the database of N items is separated into K blocks of size b = N/K elements each and an algorithm has just to find the block containing the item (of interest. The queries are exactly the same as in the standard database search problem. We present a quantum algorithm for this problem of partial search that takes about 0.34 root b fewer iterations than the quantum search algorithm.