The analysis of hashing with lazy deletions

Abstract We present new, improved algorithms for performing deletions and subsequent searches in hash tables. Our method is based on open addressing hashing extended to allow efficient reclamation of unoccupied space due to deletions which enables dynamic shortening of probe sequence lengths. We present an analysis on the number of table probes required to locate an element in the table. Specifically, we present a formula which bounds the average number of cells visited during searches of a data element over its lifetime assuming a system in equilibrium. The formula is a function of the probability that an accessed element is deleted and is exact at the extreme points when the probability is 0 and 1. In the case that the probability is 0 and the load factor is α, the number of cell visits per search access is − ln (1−α) α , and in the case that the probability is 1 the number of cell visits per search access is 1 (1−α) .