Computational geometry: an introduction
Computational geometry: an introduction
Efficient suffix trees on secondary storage
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
High-order entropy-compressed text indexes
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
A complexity theory for VLSI
Compressed representations of sequences and full-text indexes
ACM Transactions on Algorithms (TALG)
Rank and select revisited and extended
Theoretical Computer Science
Space-efficient static trees and graphs
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Orthogonal range searching in linear and almost-linear space
Computational Geometry: Theory and Applications
Succinct Orthogonal Range Search Structures on a Grid with Applications to Text Indexing
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Finding patterns in given intervals
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Range non-overlapping indexing and successive list indexing
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
A new succinct representation of RMQ-information and improvements in the enhanced suffix array
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
Range aggregate maximal points in the plane
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Space efficient data structures for dynamic orthogonal range counting
Computational Geometry: Theory and Applications
| Hi-index | 0.00 |
Let P be a set of n points that lie on an nxn grid. The well-known orthogonal range reporting problem is to preprocess P so that for any query rectangle R, we can report all points in P@?R efficiently. In many applications driven by the information retrieval or the bioinformatics communities, we do not need all the points in P@?R, but need only just the point that has the smallest y-coordinate; this motivates the study of a variation called the orthogonal range successor problem. If space is the major concern, the best-known result is by Makinen and Navarro, which requires an optimal index space of n+o(n) words and supports each query in O(logn) time. In contrast, if query time is the major concern, the best-known result is by Crochemore et al., which supports each query in O(1) time with O(n^1^+^@e) index space. In this paper, we first propose another optimal-space index with a faster O(logn/loglogn) query time. The improvement stems from the design of an index with O(1) query time when the points are restricted to lie on a narrow grid, and the subsequent application of the wavelet tree technique to support the desired query. Based on the proposed index, we directly obtain improved results for the successive indexing problem and the position-restricted pattern matching problem in the literature. We next propose an O(n^1^+^@e)-word index that supports each query in O(1) time. When compared with the result by Crochemore et al., our scheme is conceptually simpler and easier for construction. In addition, our scheme can be easily extended to work for high-dimensional cases.