On deletions in open addressing hashing

Abstract

Deletions in open addressing tables have often been seen as problematic. The usual solution is to use a special mark’deleted’ so that probe sequences continue past deleted slots, as if there was an element still sitting there. Such a solution, notwithstanding is wide applicability, may involve performance degradation. In the first part of this paper we review a practical implementation of the often overlooked deletion algorithm for linear probing hash tables, analyze its properties and performance, and provide several strong arguments in favor of the Robin Hood variant. In particular, we show how a small variation can yield substantial improvements for unsuccessful search. In the second part we propose an algorithm for true deletion in open addressing hashing with secondary clustering, like quadratic hashing. As far as we know, this is the first time that such an algorithm appears in the literature. Moreover, for tables built using the Robin Hood variant the deletion algorithm strongly preserves randomness (the resulting table is identical to the table that would result if the item were not inserted at all). Although it involves some extra memory for bookkeeping, the algorithm is comparatively easy and efficient, and it might be of some practical value, besides its theoretical interest.