3D Tiled Code Generation for Nussinov’s Algorithm

Current state-of-the-art parallel codes used to calculate the maximum number of pairs for a given RNA sequence by means of Nussinov’s algorithm do not allow for achieving speedup close up to the number of the processors used for execution of those codes on multi-core computers. This is due to the fa...

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Published inApplied sciences Vol. 12; no. 12; p. 5898
Main Authors Bielecki, Włodzimierz, Błaszyński, Piotr, Pałkowski, Marek
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.06.2022
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ISSN2076-3417
2076-3417
DOI10.3390/app12125898

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Abstract Current state-of-the-art parallel codes used to calculate the maximum number of pairs for a given RNA sequence by means of Nussinov’s algorithm do not allow for achieving speedup close up to the number of the processors used for execution of those codes on multi-core computers. This is due to the fact that known codes do not make full use of and derive benefit from cache memory of such computers. There is a need to develop new approaches allowing for increasing cache exploitation in multi-core computers. One of such possibilities is increasing the dimension of tiles in generated target tiled code and assuring a similar size of generated tiles. The article presents an approach allowing us to produce 3D parallel code with tiling calculating Nussinov’s RNA folding, i.e., code with the maximal tile dimension possible for the loop nest, executing Nussinov’s algorithm. The approach guarantees that generated tiles are of a similar size. The code generated with the presented approach is characterized by increased code locality and outperforms all closely related ones examined by us. This allows us to considerably reduce execution time required for computing the maximum number of pairs of any nested structure for larger RNA sequences by means of Nussinov’s algorithm.
AbstractList Current state-of-the-art parallel codes used to calculate the maximum number of pairs for a given RNA sequence by means of Nussinov’s algorithm do not allow for achieving speedup close up to the number of the processors used for execution of those codes on multi-core computers. This is due to the fact that known codes do not make full use of and derive benefit from cache memory of such computers. There is a need to develop new approaches allowing for increasing cache exploitation in multi-core computers. One of such possibilities is increasing the dimension of tiles in generated target tiled code and assuring a similar size of generated tiles. The article presents an approach allowing us to produce 3D parallel code with tiling calculating Nussinov’s RNA folding, i.e., code with the maximal tile dimension possible for the loop nest, executing Nussinov’s algorithm. The approach guarantees that generated tiles are of a similar size. The code generated with the presented approach is characterized by increased code locality and outperforms all closely related ones examined by us. This allows us to considerably reduce execution time required for computing the maximum number of pairs of any nested structure for larger RNA sequences by means of Nussinov’s algorithm.
Author Pałkowski, Marek
Bielecki, Włodzimierz
Błaszyński, Piotr
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Cites_doi 10.1016/B978-0-12-384988-5.00014-0
10.1093/nar/9.1.133
10.1186/s12859-017-1707-8
10.1016/0022-2836(81)90087-5
10.1186/s12859-017-1917-0
10.1186/1471-2105-15-S8-S1
10.1145/2400682.2400713
10.1109/IPDPS.2011.186
10.1007/978-3-642-15582-6_49
10.1109/ASAP.2008.4580177
10.1186/1471-2105-10-S1-S37
10.1186/s12859-019-2785-6
10.1137/0135006
10.1186/s12859-018-2008-6
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References Smith (ref_17) 1981; 147
ref_14
Nussinov (ref_5) 1978; 35
ref_13
ref_12
ref_11
Wonnacott (ref_2) 2013; 2013
ref_10
Xia (ref_15) 2009; 10
ref_1
Verdoolaege (ref_20) 2013; 9
Palkowski (ref_21) 2018; 19
Palkowski (ref_4) 2019; 20
Li (ref_18) 2014; 15
ref_9
Zuker (ref_16) 1981; 9
Zhao (ref_19) 2017; 18
ref_8
Palkowski (ref_3) 2017; 18
ref_7
ref_6
References_xml – ident: ref_14
  doi: 10.1016/B978-0-12-384988-5.00014-0
– ident: ref_6
– ident: ref_9
– ident: ref_8
– volume: 9
  start-page: 133
  year: 1981
  ident: ref_16
  article-title: Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information
  publication-title: Nucleic Acids Res.
  doi: 10.1093/nar/9.1.133
– volume: 18
  start-page: 1
  year: 2017
  ident: ref_3
  article-title: Parallel tiled Nussinov RNA folding loop nest generated using both dependence graph transitive closure and loop skewing
  publication-title: BMC Bioinform.
  doi: 10.1186/s12859-017-1707-8
– volume: 147
  start-page: 195
  year: 1981
  ident: ref_17
  article-title: Identification of common molecular subsequences
  publication-title: J. Mol. Biol.
  doi: 10.1016/0022-2836(81)90087-5
– volume: 18
  start-page: 15
  year: 2017
  ident: ref_19
  article-title: Cache and energy efficient algorithms for nussinov’s rna folding
  publication-title: BMC Bioinform.
  doi: 10.1186/s12859-017-1917-0
– ident: ref_10
– volume: 15
  start-page: 1
  year: 2014
  ident: ref_18
  article-title: Multicore and GPU algorithms for Nussinov RNA folding
  publication-title: BMC Bioinform.
  doi: 10.1186/1471-2105-15-S8-S1
– volume: 9
  start-page: 1
  year: 2013
  ident: ref_20
  article-title: Polyhedral parallel code generation for CUDA
  publication-title: ACM Trans. Archit. Code Optim. (TACO)
  doi: 10.1145/2400682.2400713
– ident: ref_12
  doi: 10.1109/IPDPS.2011.186
– ident: ref_7
  doi: 10.1007/978-3-642-15582-6_49
– ident: ref_11
  doi: 10.1109/ASAP.2008.4580177
– volume: 10
  start-page: 1
  year: 2009
  ident: ref_15
  article-title: Fine-grained parallel RNAalifold algorithm for RNA secondary structure prediction on FPGA
  publication-title: BMC Bioinform.
  doi: 10.1186/1471-2105-10-S1-S37
– ident: ref_13
– ident: ref_1
– volume: 2013
  start-page: 3
  year: 2013
  ident: ref_2
  article-title: On the scalability of loop tiling techniques
  publication-title: IMPACT
– volume: 20
  start-page: 1
  year: 2019
  ident: ref_4
  article-title: Tiling Nussinov’s RNA folding loop nest with a space-time approach
  publication-title: BMC Bioinform.
  doi: 10.1186/s12859-019-2785-6
– volume: 35
  start-page: 68
  year: 1978
  ident: ref_5
  article-title: Algorithms for loop matchings
  publication-title: SIAM J. Appl. Math.
  doi: 10.1137/0135006
– volume: 19
  start-page: 1
  year: 2018
  ident: ref_21
  article-title: Tuning iteration space slicing based tiled multi-core code implementing Nussinov’s RNA folding
  publication-title: BMC Bioinform.
  doi: 10.1186/s12859-018-2008-6
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SubjectTerms Algorithms
bioinformatics
Codes
compiler
Dynamic programming
nussinov
RNA
shared memory algorithms
source code generation
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