Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
On finding lowest common ancestors: simplification and parallelization
SIAM Journal on Computing
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
A unifying look at data structures
Communications of the ACM
Programming pearls: algorithm design techniques
Communications of the ACM
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Journal of Computer and System Sciences - Computational biology 2002
A Linear Time Algorithm for Finding All Maximal Scoring Subsequences
Proceedings of the Seventh International Conference on Intelligent Systems for Molecular Biology
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
An Optimal Algorithm for the Maximum-Density Segment Problem
SIAM Journal on Computing
Lowest common ancestors in trees and directed acyclic graphs
Journal of Algorithms
Information Processing Letters
An optimal algorithm for maximum-sum segment and its application in bioinformatics
CIAA'03 Proceedings of the 8th international conference on Implementation and application of automata
Optimal algorithms for the average-constrained maximum-sum segment problem
Information Processing Letters
Hi-index | 0.05 |
The range minimum query problem, RMQ for short, is to preprocess a sequence of real numbers A[1...n] for subsequent queries of the form: "Given indices i, j, what is the index of the minimum value of A[i...j]?" This problem has been shown to be linearly equivalent to the LCA problem in which a tree is preprocessed for answering the lowest common ancestor of two nodes. It has also been shown that both the RMQ and LCA problems can be solved in linear preprocessing time and constant query time under the unit-cost RAM model. This paper studies a new query problem arising from the analysis of biological sequences. Specifically, we wish to answer queries of the form: "Given indices i and j, what is the maximum-sum segment of A[i...j]?" We establish the linear equivalence relation between RMQ and this new problem. As a consequence, we can solve the new query problem in linear preprocessing time and constant query time under the unit-cost RAM model. We then present alternative linear-time solutions for two other biological sequence analysis problems to demonstrate the utilities of the techniques developed in this paper.