TY - GEN

T1 - Partial covering arrays

T2 - 27th International Workshop on Combinatorial Algorithms, IWOCA 2016

AU - Sarkar, Kaushik

AU - Colbourn, Charles

AU - De Bonis, Annalisa

AU - Vaccaro, Ugo

N1 - Funding Information:
Research of KS and CJC was supported in part by the National Science Foundation under Grant No. 1421058.
Publisher Copyright:
© Springer International Publishing Switzerland 2016.

PY - 2016/7/1

Y1 - 2016/7/1

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 - 10.1007/978-3-319-44543-4_34

DO - 10.1007/978-3-319-44543-4_34

M3 - Conference contribution

AN - SCOPUS:84984914877

SN - 9783319445427

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

A2 - Mäkinen, Veli

A2 - Puglisi, Simon J.

A2 - Salmela, Leena

PB - Springer Verlag

Y2 - 17 August 2016 through 19 August 2016

ER -