Strongly History-Independent Hashing with Applications

Abstract

We present a strongly history independent (SHI) hash table that supports search in O(1) worst-case time, and insert and delete in O(1) expected time using O(n) data space. This matches the bounds for dynamic perfect hashing, and improves on the best previous results by Naor and Teague on history independent hashing, which were either weakly history independent, or only supported insertion and search (no delete) each in O(1) expected time.The results can be used to construct many other SHI data structures. We show straightforward constructions for SHI ordered dictionaries: for n keys from {1, . . . , n k } searches take O(log log n) worst-case time and updates (insertions and deletions) O(log log n) expected time, and for keys in the comparison model searches take O(log n) worst-case time and updates O(log n) expected time. We also describe a SHI data structure for the order-maintenance problem. It supports comparisons in O(1) worst-case time, and updates in O(1) expected time. All structures use O(n) data space.

Hifs

“…(1) -(5) ensure that the layout of keys in the hash table is the same irrespective of the sequence of key insertions and deletions, thereby making it history independent [5].…”

“…The data structure of choice here is the history independent hash table in [5]. Hence, first we describe the hash table construction and in subsequent sections illustrate its use in various HIFS components.…”

“…The re-ordering of preferences leads to the realization that we can rewrite the algorithms in [5] to enable easy-custom selection of history independent layouts with minimal modifications. For this, we categorize the hash table operations in two Procedure Sets, a generic set and a customizable set.…”

“…The hash table in [5] is based on the stable matching property of the Gale-Shapley Stable Marriage algorithm [10] detailed in the following.…”

“…Although prior work has focussed on designing history independent 1 data structures [5,8,12,13,16,19], many challenges remain un-addressed for their successful deployment in systems. The first challenge is the un-availability of systemwide, space-allocation mechanisms that are also history independent.…”