Range minimum queries (RMQs) are essential in many algorithmic procedures. The problem is to prepare a data structure on an array to allow for fast subsequent queries that find the minimum within a range in the array. We study the problem of designing indexing RMQ data structures which only require sub-linear space and access to the input array while querying. The RMQ problem in one-dimensional arrays is well understood with known indexing data structures achieving optimal space and query time. The two-dimensional indexing RMQ data structures have received the attention of researchers recently. There are also several solutions for the RMQ problem in higher dimensions. Yuan and Atallah [SODA’10] designed a brilliant data structure of size O(N) which supports RMQs in a multi-dimensional array of size N in constant time for a constant number of dimensions. In this paper we consider the problem of designing indexing data structures for RMQs in higher dimensions. We design a data structure of size O(N) bits that supports RMQs in constant time for a constant number of dimensions. We also show how to obtain trade-offs between the space of indexing data structures and their query time.
|Title of host publication||Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings|
|Editors||Ugo Vaccaro, Ely Porat, Ferdinando Cicalese|
|Number of pages||11|
|State||Published - 2015|
|Event||26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015 - Ischia Island, Italy|
Duration: 29 Jun 2015 → 1 Jul 2015
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015|
|Period||29/06/15 → 1/07/15|
Bibliographical noteFunding Information:
M. Lewenstein—Research supported by BSF grant 2010437, a Google Research Award and GIF grant 1147/2011.
J. Iacono—Research supported by NSF grant CCF-1018370 and BSF grant 2010437.
G.M. Landau—Research partially supported by the National Science Foundation Award 0904246, Israel Science Foundation grant 571/14, Grant No. 2008217 from the United States- Israel Binational Science Foundation (BSF) and DFG.
© Springer International Publishing Switzerland 2015.
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science (all)