Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
On finding lowest common ancestors: simplification and parallelization
SIAM Journal on Computing
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Algorithms for Reporting and Counting Geometric Intersections
IEEE Transactions on Computers
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Video sequence matching based on temporal ordinal measurement
Pattern Recognition Letters
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
Lowest common ancestors in trees and directed acyclic graphs
Journal of Algorithms
Journal of Biomedical Informatics
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The trend of a time series can be represented as a ranking sequence, which reveals the ups and downs with the passage of time. In some applications, one might need to find the trend in some specific period of time or search for the period of time with some specific trend. We formulate three related problems: the local ranking problem, the local ranking sequence problem and the ranking sequence matching problem. The first two are to find the rankings given a segment of the time sequence and the last one is to search for the matching positions to the query sequence. For all the problems, we propose different algorithms utilizing a modified segment tree data structure. It takes O(nlogn) time and space to build the segment tree where n is the length of the target ranking sequence. The query time of the three algorithms are O(logk), O(k) and O(nlogk), respectively, where k is the size of the query range.