Fast RSK Correspondence by Doubling Search

The Robinson-Schensted-Knuth (RSK) correspondence is a fundamental concept in combinatorics and representation theory. It is defined as a certain bijection between permutations and pairs of Young tableaux of a given order. We consider the RSK correspondence as an algorithmic problem, along with the closely related k-chain problem. We give a simple, direct description of the symmetric RSK algorithm, which is implied by the k-chain algorithms of Viennot and of Felsner and Wernisch. We also show how the doubling search of Bentley and Yao can be used as a subroutine by the symmetric RSK algorithm, replacing the default binary search. Surprisingly, such a straightforward replacement improves the asymptotic worst-case running time for the RSK correspondence that has been best known since 1998. A similar improvement also holds for the average running time of RSK on uniformly random permutations

Bounded-Length Smith-Waterman Alignment

Given a fixed alignment scoring scheme, the bounded length (respectively, bounded total length) Smith-Waterman alignment problem on a pair of strings of lengths m, n, asks for the maximum alignment score across all substring pairs, such that the first substring\u27s length (respectively, the sum of the two substrings\u27 lengths) is above the given threshold w. The latter problem was introduced by Arslan and Egecioglu under the name "local alignment with length threshold". They proposed a dynamic programming algorithm solving the problem in time O(mn^2), and also an approximation algorithm running in time O(rmn), where r is a parameter controlling the accuracy of approximation. We show that both these problems can be solved exactly in time O(mn), assuming a rational scoring scheme; furthermore, this solution can be used to obtain an exact algorithm for the normalised bounded total length Smith - Waterman alignment problem, running in time O(mn log n). Our algorithms rely on the techniques of fast window-substring alignment and implicit unit-Monge matrix searching, developed previously by the author and others

Bounded-length Smith-Waterman alignment

Given a fixed alignment scoring scheme, the bounded length (respectively, bounded total length) Smith-Waterman alignment problem on a pair of strings of lengths m, n, asks for the maximum alignment score across all substring pairs, such that the first substring's length (respectively, the sum of the two substrings' lengths) is above the given threshold w. The latter problem was introduced by Arslan and Egecioglu under the name "local alignment with length threshold". They proposed a dynamic programming algorithm solving the problem in time O(mn^2), and also an approximation algorithm running in time O(rmn), where r is a parameter controlling the accuracy of approximation. We show that both these problems can be solved exactly in time O(mn), assuming a rational scoring scheme; furthermore, this solution can be used to obtain an exact algorithm for the normalised bounded total length Smith - Waterman alignment problem, running in time O(mn log n). Our algorithms rely on the techniques of fast window-substring alignment and implicit unit-Monge matrix searching, developed previously by the author and others

Computing alignment plots efficiently

Dot plots are a standard method for local comparison of biological sequences. In a dot plot, a substring to substring distance is computed for all pairs of fixed-size windows in the input strings. Commonly, the Hamming distance is used since it can be computed in linear time. However, the Hamming distance is a rather crude measure of string similarity, and using an alignment-based edit distance can greatly improve the sensitivity of the dot plot method. In this paper, we show how to compute alignment plots of the latter type efficiently. Given two strings of length m and n and a window size w, this problem consists in computing the edit distance between all pairs of substrings of length w, one from each input string. The problem can be solved by repeated application of the standard dynamic programming algorithm in time O(mnw^2). This paper gives an improved data-parallel algorithm, running in time $O(mnw/\gamma/p)$ using vector operations that work on $\gamma$ values in parallel and $p$ processors. We show experimental results from an implementation of this algorithm, which uses Intel's MMX/SSE instructions for vector parallelism and MPI for coarse-grained parallelism.Comment: Presented at ParCo 200

Conserved noncoding sequences highlight shared components of regulatory networks in dicotyledonous plants

Conserved noncoding sequences (CNSs) in DNA are reliable pointers to regulatory elements controlling gene expression. Using a comparative genomics approach with four dicotyledonous plant species (Arabidopsis thaliana, papaya [Carica papaya], poplar [Populus trichocarpa], and grape [Vitis vinifera]), we detected hundreds of CNSs upstream of Arabidopsis genes. Distinct positioning, length, and enrichment for transcription factor binding sites suggest these CNSs play a functional role in transcriptional regulation. The enrichment of transcription factors within the set of genes associated with CNS is consistent with the hypothesis that together they form part of a conserved transcriptional network whose function is to regulate other transcription factors and control development. We identified a set of promoters where regulatory mechanisms are likely to be shared between the model organism Arabidopsis and other dicots, providing areas of focus for further research

State-of-the-art in string similarity search and join

String similarity search and its variants are fundamental problems with many applications in areas such as data integration, data quality, computational linguistics, or bioinformatics. A plethora of methods have been developed over the last decades. Obtaining an overview of the state-of-the-art in this field is difficult, as results are published in various domains without much cross-talk, papers use different data sets and often study subtle variations of the core problems, and the sheer number of proposed methods exceeds the capacity of a single research group. In this paper, we report on the results of the probably largest benchmark ever performed in this field. To overcome the resource bottleneck, we organized the benchmark as an international competition, a workshop at EDBT/ICDT 2013. Various teams from different fields and from all over the world developed or tuned programs for two crisply defined problems. All algorithms were evaluated by an external group on two machines. Altogether, we compared 14 different programs on two string matching problems (k-approximate search and k-approximate join) using data sets of increasing sizes and with different characteristics from two different domains. We compare programs primarily by wall clock time, but also provide results on memory usage, indexing time, batch query effects and scalability in terms of CPU cores. Results were averaged over several runs and confirmed on a second, different hardware platform. A particularly interesting observation is that disciplines can and should learn more from each other, with the three best teams rooting in computational linguistics, databases, and bioinformatics, respectively