scholarly journals A Linear Time and Space Algorithm for Detecting Path Intersection

2009 ◽  
pp. 397-408
Author(s):  
Srečko Brlek ◽  
Michel Koskas ◽  
Xavier Provençal
Keyword(s):  
Linear Time ◽  
Time And Space

Toward accurate dynamic time warping in linear time and space

2007 ◽  
Vol 11 (5) ◽  
pp. 561-580 ◽  
Author(s):  
Stan Salvador ◽  
Philip Chan
Keyword(s):  
Dynamic Time Warping ◽  
Linear Time ◽  
Time Warping ◽  
Time And Space ◽  
Dynamic Time

scholarly journals Invariant subspace method: A tool for solving fractional partial differential equations

2017 ◽  
Vol 20 (2) ◽  
Author(s):  
Sangita Choudhary ◽  
Varsha Daftardar-Gejji
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Invariant Subspace ◽  
Caputo Derivative ◽  
Linear Time ◽  
Subspace Method ◽  
Fractional Partial Differential Equations ◽  
Time And Space ◽  
Partial Differential ◽  
Non Linear

AbstractIn this paper invariant subspace method has been employed for solving linear and non-linear time and space fractional partial differential equations involving Caputo derivative. A variety of illustrative examples are solved to demonstrate the effectiveness and applicability of the method.

scholarly journals MONI: A Pangenomics Index for Finding MEMs

2021 ◽  
Author(s):  
Massimiliano Rossi ◽  
Marco Oliva ◽  
Ben Langmead ◽  
Travis Gagie ◽  
Christina Boucher
Keyword(s):  
Pattern Matching ◽  
Linear Time ◽  
Repetitive Sequences ◽  
Major Advance ◽  
Human Chromosomes ◽  
Time And Space ◽  
Index Construction ◽  
Approximate Pattern Matching ◽  
Human Genomes ◽  
Novel Algorithm

Recently, Gagie et al. proposed a version of the FM-index, called the r-index, that can store thousands of human genomes on a commodity computer. Then Kuhnle et al. showed how to build the r-index efficiently via a technique called prefix-free parsing (PFP) and demonstrated its effectiveness for exact pattern matching. Exact pattern matching can be leveraged to support approximate pattern matching but the r-index itself cannot support efficiently popular and important queries such as finding maximal exact matches (MEMs). To address this shortcoming, Bannai et al. introduced the concept of thresholds, and showed that storing them together with the r-index enables efficient MEM finding --- but they did not say how to find those thresholds. We present a novel algorithm that applies PFP to build the r-index and find the thresholds simultaneously and in linear time and space with respect to the size of the prefix-free parse. Our implementation called MONI can rapidly find MEMs between reads and large sequence collections of highly repetitive sequences. Compared to other read aligners -- PuffAligner, Bowtie2, BWA-MEM, and CHIC -- MONI used 2--11 times less memory and was 2--32 times faster for index construction. Moreover, MONI was less than one thousandth the size of competing indexes for large collections of human chromosomes. Thus, MONI represents a major advance in our ability to perform MEM finding against very large collections of related references. Availability: MONI is publicly available at https://github.com/maxrossi91/moni.

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