Compact dynamic rewritable (CDRW) arrays

Abstract

In this paper we consider the problem of compactly representing a rewritable array of bit-strings. The operations supported are: create(N; k), which creates a new array of size N, where each entry is of size at most k bits and equal to 0; set(i; v), which sets A[i] to v, provided that v is at most k bits long and get(i) which returns the value of A[i]. Our aim is to approach the minimum possible space bound of S = σN-1i=0 jA[i]j, where jA[i]j ≥ 1 is the length in bits of the number in A[i], while simultaneously supporting operations in O(1) time. We call such a data structure a Compact Dynamic Rewriteable Array (CDRW) array. On the word RAM model with word size w, for n < 2w and k ≤ w, we give practical solutions based on compact hashing that achieve O(1=ϵ) expected time for get and set and use (1 + ϵ)S + O(N) bits, for any constant ϵ < 0. Experimental evaluation of our (preliminary, only somewhat optimized) implementations shows excellent performance in terms of both space and time, particularly when heuristics are added to our base algorithms.