Practical Entropy-Bounded Schemes for O(1)-Range Minimum Queries

The Range Minimum Query (RMQ) Problem is to preprocess an array A of length n in O(n) time such that subsequent on-line queries asking for the position of a minimal element between two specified indices can be obtained in constant time. Several solutions to this problem have been proposed, starting with Berkman and Vishkin's linear-space solution [6], and leading to a succinct solution using only 2n+ o(n) bits in addition to the input array [12]. The theoretical contribution of this article is to push this latter approach one step further and show that for compressible input arrays the RMQ-information can be compressed as well. In particular, we show that information for O(1)-RMQs can be stored within the same entropy bounds that are achieved by the currently best schemes for storing A itself in compressed form, while still being able to access O(log n) contiguous bits in O(1) time [10]. Two such entropybounded schemes for O(1)-RMQs are developed, each with its own practical advan...

• Type: Conference
• Year: 2008
• Where: DCC
• Authors: Johannes Fischer, Volker Heun, Horst Martin Stühler
• Keywords: Compressible Input Arrays, Computer Graphics, DCC 2008, Non-compressed Schemes, Succinct Solution