Partial covering arrays: Algorithms and asymptotics

Kaushik Sarkar, Charles Colbourn, Annalisa De Bonis, Ugo Vaccaro

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

6 Citations (Scopus)

Abstract

A covering array CA(N; t, k, v) is an N ×k array with entries in {1, 2, … , v}, for which every N × t subarray contains each t-tuple of {1, 2, … , v}t among its rows.Covering arrays find application in interaction testing, including software and hardware testing, advanced materials development, and biological systems.A central question is to determine or bound CAN(t, k, v), the minimum number N of rows of a CA(N; t, k, v).The well known bound CAN(t, k, v) = O((t − 1)vt log k) is not too far from being asymptotically optimal.Sensible relaxations of the covering requirement arise when (1) the set {1, 2, … , v}t need only be contained among the rows of at least (1 − ϵ)(k t) of the N × t subarrays and (2) the rows of every N × t subarray need only contain a (large) subset of {1, 2, … , v}t.In this paper, using probabilistic methods, significant improvements on the covering array upper bound are established for both relaxations, and for the conjunction of the two.In each case, a randomized algorithm constructs such arrays in expected polynomial time.

Original languageEnglish (US)
Title of host publicationCombinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings
PublisherSpringer Verlag
Pages437-448
Number of pages12
Volume9843
ISBN (Print)9783319445427
DOIs
StatePublished - 2016
Event27th International Workshop on Combinatorial Algorithms, IWOCA 2016 - Helsinki, Finland
Duration: Aug 17 2016Aug 19 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9843
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other27th International Workshop on Combinatorial Algorithms, IWOCA 2016
CountryFinland
CityHelsinki
Period8/17/168/19/16

Fingerprint

Covering Array
Software testing
Biological systems
Computer hardware
Polynomials
Partial
Testing
Software Testing
Probabilistic Methods
Randomized Algorithms
Asymptotically Optimal
Biological Systems
Polynomial time
Covering
Hardware
Upper bound
Subset
Requirements
Interaction

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Sarkar, K., Colbourn, C., De Bonis, A., & Vaccaro, U. (2016). Partial covering arrays: Algorithms and asymptotics. In Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings (Vol. 9843, pp. 437-448). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9843). Springer Verlag. https://doi.org/10.1007/978-3-319-44543-434

Partial covering arrays : Algorithms and asymptotics. / Sarkar, Kaushik; Colbourn, Charles; De Bonis, Annalisa; Vaccaro, Ugo.

Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings. Vol. 9843 Springer Verlag, 2016. p. 437-448 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9843).

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

Sarkar, K, Colbourn, C, De Bonis, A & Vaccaro, U 2016, Partial covering arrays: Algorithms and asymptotics. in Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings. vol. 9843, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9843, Springer Verlag, pp. 437-448, 27th International Workshop on Combinatorial Algorithms, IWOCA 2016, Helsinki, Finland, 8/17/16. https://doi.org/10.1007/978-3-319-44543-434
Sarkar K, Colbourn C, De Bonis A, Vaccaro U. Partial covering arrays: Algorithms and asymptotics. In Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings. Vol. 9843. Springer Verlag. 2016. p. 437-448. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-44543-434
Sarkar, Kaushik ; Colbourn, Charles ; De Bonis, Annalisa ; Vaccaro, Ugo. / Partial covering arrays : Algorithms and asymptotics. Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings. Vol. 9843 Springer Verlag, 2016. pp. 437-448 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{db11735fcc494466a33b49a32cc5951e,
title = "Partial covering arrays: Algorithms and asymptotics",
abstract = "A covering array CA(N; t, k, v) is an N ×k array with entries in {1, 2, … , v}, for which every N × t subarray contains each t-tuple of {1, 2, … , v}t among its rows.Covering arrays find application in interaction testing, including software and hardware testing, advanced materials development, and biological systems.A central question is to determine or bound CAN(t, k, v), the minimum number N of rows of a CA(N; t, k, v).The well known bound CAN(t, k, v) = O((t − 1)vt log k) is not too far from being asymptotically optimal.Sensible relaxations of the covering requirement arise when (1) the set {1, 2, … , v}t need only be contained among the rows of at least (1 − ϵ)(k t) of the N × t subarrays and (2) the rows of every N × t subarray need only contain a (large) subset of {1, 2, … , v}t.In this paper, using probabilistic methods, significant improvements on the covering array upper bound are established for both relaxations, and for the conjunction of the two.In each case, a randomized algorithm constructs such arrays in expected polynomial time.",
author = "Kaushik Sarkar and Charles Colbourn and {De Bonis}, Annalisa and Ugo Vaccaro",
year = "2016",
doi = "10.1007/978-3-319-44543-434",
language = "English (US)",
isbn = "9783319445427",
volume = "9843",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "437--448",
booktitle = "Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings",
address = "Germany",

}

TY - GEN

T1 - Partial covering arrays

T2 - Algorithms and asymptotics

AU - Sarkar, Kaushik

AU - Colbourn, Charles

AU - De Bonis, Annalisa

AU - Vaccaro, Ugo

PY - 2016

Y1 - 2016

N2 - A covering array CA(N; t, k, v) is an N ×k array with entries in {1, 2, … , v}, for which every N × t subarray contains each t-tuple of {1, 2, … , v}t among its rows.Covering arrays find application in interaction testing, including software and hardware testing, advanced materials development, and biological systems.A central question is to determine or bound CAN(t, k, v), the minimum number N of rows of a CA(N; t, k, v).The well known bound CAN(t, k, v) = O((t − 1)vt log k) is not too far from being asymptotically optimal.Sensible relaxations of the covering requirement arise when (1) the set {1, 2, … , v}t need only be contained among the rows of at least (1 − ϵ)(k t) of the N × t subarrays and (2) the rows of every N × t subarray need only contain a (large) subset of {1, 2, … , v}t.In this paper, using probabilistic methods, significant improvements on the covering array upper bound are established for both relaxations, and for the conjunction of the two.In each case, a randomized algorithm constructs such arrays in expected polynomial time.

AB - A covering array CA(N; t, k, v) is an N ×k array with entries in {1, 2, … , v}, for which every N × t subarray contains each t-tuple of {1, 2, … , v}t among its rows.Covering arrays find application in interaction testing, including software and hardware testing, advanced materials development, and biological systems.A central question is to determine or bound CAN(t, k, v), the minimum number N of rows of a CA(N; t, k, v).The well known bound CAN(t, k, v) = O((t − 1)vt log k) is not too far from being asymptotically optimal.Sensible relaxations of the covering requirement arise when (1) the set {1, 2, … , v}t need only be contained among the rows of at least (1 − ϵ)(k t) of the N × t subarrays and (2) the rows of every N × t subarray need only contain a (large) subset of {1, 2, … , v}t.In this paper, using probabilistic methods, significant improvements on the covering array upper bound are established for both relaxations, and for the conjunction of the two.In each case, a randomized algorithm constructs such arrays in expected polynomial time.

UR - http://www.scopus.com/inward/record.url?scp=84984914877&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84984914877&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-44543-434

DO - 10.1007/978-3-319-44543-434

M3 - Conference contribution

AN - SCOPUS:84984914877

SN - 9783319445427

VL - 9843

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 437

EP - 448

BT - Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings

PB - Springer Verlag

ER -