The Analysis of Hashing Techniques That Exhibit k-ary Clustering

In this paper we relate the performance of hashmg algonthms to the notion of clustering, that is, the pile-up phenomenon that occurs because many keys may probe the table locations m the same sequence We will say that a hashmg technique exhibits k-ary clustering if the search for a key begins with k independent random probes and the subsequent sequence of probes is completely determined by the location of the k initial probes Such techniques may be very bad, for instance, the average number of probes necessary for mseruon may grow linearly with the table size However, on the average (that is if the permutations describing the method are randomly chosen), k-ary clustering techniques for k > 1 are very good. In fact the average performance is asymptotically equivalent to the performance of umform probing, a method that exhibits no clustering and is known to be optimal in a certain sense.