Sequence covering arrays and linear extensions

Patrick C. Murray, Charles Colbourn

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

Covering subsequences by sets of permutations arises in numerous applications. Given a set of permutations that cover a specific set of subsequences, it is of interest not just to know how few permutations can be used, but also to find a set of size equal to or close to the minimum. These permutation construction problems have proved to be computationally challenging; few explicit constructions have been found for small sets of permutations of intermediate length, mostly arising from greedy algorithms. A different strategy is developed here. Starting with a set that covers the specific subsequences required, we determine local changes that can be made in the permutations without losing the required coverage. By selecting these local changes (using linear extensions) so as to make one or more permutations less ‘important’ for coverage, the method attempts to make a permutation redundant so that it can be removed and the set size reduced. A post-optimization method to do this is developed, and preliminary results on sequence covering arrays show that it is surprisingly effective.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages274-285
Number of pages12
Volume8986
ISBN (Print)9783319193144
DOIs
StatePublished - 2015
Event25th International Workshop on Combinatorial Algorithms, IWOCA 2014 - Duluth, United States
Duration: Oct 15 2014Oct 17 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8986
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other25th International Workshop on Combinatorial Algorithms, IWOCA 2014
CountryUnited States
CityDuluth
Period10/15/1410/17/14

Fingerprint

Covering Array
Linear Extension
Permutation
Subsequence
Coverage
Set Cover
Greedy Algorithm
Optimization Methods
Covering
Cover

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Murray, P. C., & Colbourn, C. (2015). Sequence covering arrays and linear extensions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8986, pp. 274-285). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8986). Springer Verlag. https://doi.org/10.1007/978-3-319-19315-1_24

Sequence covering arrays and linear extensions. / Murray, Patrick C.; Colbourn, Charles.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8986 Springer Verlag, 2015. p. 274-285 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8986).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Murray, PC & Colbourn, C 2015, Sequence covering arrays and linear extensions. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 8986, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8986, Springer Verlag, pp. 274-285, 25th International Workshop on Combinatorial Algorithms, IWOCA 2014, Duluth, United States, 10/15/14. https://doi.org/10.1007/978-3-319-19315-1_24
Murray PC, Colbourn C. Sequence covering arrays and linear extensions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8986. Springer Verlag. 2015. p. 274-285. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-19315-1_24
Murray, Patrick C. ; Colbourn, Charles. / Sequence covering arrays and linear extensions. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8986 Springer Verlag, 2015. pp. 274-285 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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