Showing papers by "Rolf Fagerberg published in 2009"
05 Dec 2009
TL;DR: A data structure in the RAM model is presented supporting queries that given two indices i ≤ j and an integer k report the k smallest elements in the subarray A[i..j] in sorted order in optimal O(k) time.
Abstract: We study the following one-dimensional range reporting problem: On an array A of n elements, support queries that given two indices i ≤ j and an integer k report the k smallest elements in the subarray A[i..j] in sorted order. We present a data structure in the RAM model supporting such queries in optimal O(k) time. The structure uses O(n) words of space and can be constructed in O(n logn) time. The data structure can be extended to solve the online version of the problem, where the elements in A[i..j] are reported one-by-one in sorted order, in O(1) worst-case time per element. The problem is motivated by (and is a generalization of) a problem with applications in search engines: On a tree where leaves have associated rank values, report the highest ranked leaves in a given subtree. Finally, the problem studied generalizes the classic range minimum query (RMQ) problem on arrays.
54 citations
TL;DR: This work significantly improves the space bounds of the Ziv-Lempel adaptive dictionary compression schemes, improving the previously known complexities for both approximate string matching and regular expression matching problems.
Abstract: We study the approximate string matching and regular expression matching problem for the case when the text to be searched is compressed with the Ziv-Lempel adaptive dictionary compression schemes. We present a time-space trade-off that leads to algorithms improving the previously known complexities for both problems. In particular, we significantly improve the space bounds, which in practical applications are likely to be a bottleneck.
27 citations
01 Jan 2009
TL;DR: Heuristics for speeding up the neighbour-joining method which generate the same phylogenetic trees as the original method, showing that the presented heuristics can give a significant speed-up over the standard neighbour- joining method, already for medium sized instances.
Abstract: A widely used method for constructing phylogenetic trees is the neighbour-joining method of Saitou and Nei. We develope heuristics for speeding up the neighbour-joining method which generate the same phylogenetic trees as the original method. All heuristics are based on using a quad-tree to guide the search for the next pair of nodes to join, but differ in the information stored in quad-tree nodes, the way the search is performed, and in the way the quad-tree is updated after a join. We empirically evaluate the performance of the heuristics on distance matrices obtained from the Pfam collection of alignments, and compare the running time with that of the QuickTree tool, a well-known and widely used implementation of the standard neighbour-joining method. The results show that the presented heuristics can give a significant speed-up over the standard neighbour-joining method, already for medium sized instances.
1 citations