Compressed Data Structures: Dictionaries and Data-Aware Measures

Abstract. We propose measures for compressed data structures, in which space usage is measured in a data-aware manner. In particular, we consider the fundamental dictionary problem on set data, where the task is to construct a data structure to represent a set S of n items out of a universe U = {0, . . . , u - 1} and support various queries on S. We use a well-known data-aware measure for set data called gap to bound the space of our data structures. We describe a novel dictionary structure taking gap+O(n log(u/n)/ log n)+O(n log log(u/n)) bits. Under the RAM model, our dictionary supports membership, rank, select, and predecessor queries in nearly optimal time, matching the time bound of Andersson and Thorup's predecessor structure [AT00], while simultaneously improving upon their space usage. Our dictionary structure uses exactly gap bits in the leading term (i.e., the constant factor is 1) and answers queries in near-optimal time. When seen from the worst case perspective, we p...

• Type: Conference
• Year: 2006
• Where: DCC
• Authors: Ankur Gupta, Wing-Kai Hon, Rahul Shah, Jeffrey Scott Vitter
• Keywords: Computer Graphics, Data-aware Space Usage, DCC 2006, Log(u/n))-bit Dictionary Structure, Partial Rank Queries