Sequence Covering Arrays and Linear Extensions
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.
Thanks to Sunil Chandran, Marty Golumbic, Rogers Mathew, and Deepak Rajendraprasad for interesting discussions about permutation coverings and geometric representations of graphs and hypergraphs.
- 1.Banbara, M., Tamura, N., Inoue, K.: Generating event-sequence test cases by answer set programming with the incidence matrix. In: Technical Communications of the 28th International Conference on Logic Programming (ICLP 2012), pp. 86–97 (2012)Google Scholar
- 3.Brain, M., Erdem, E., Inoue, K., Oetsch, J., Pührer, J., Tompits, H., Yilmaz, C.: Event-sequence testing using answer-set programming. Int. J. Adv. Softw. 5(3–4), 237–251 (2012)Google Scholar
- 9.Erdem, E., Inoue, K., Oetsch, J., Pührer, J., Tompits, H., Yilmaz, C.: Answer-set programming as a new approach to event-sequence testing. In: Proceedings of the Second International Conference on Advances in System Testing and Validation Lifecycle, pp. 25–34. Xpert Publishing Services (2011)Google Scholar
- 12.Hazli, M.M.Z., Zamli, K.Z., Othman, R.R.: Sequence-based interaction testing implementation using bees algorithm. In: 2012 IEEE Symposium on Computers and Informatics, pp. 81–85. IEEE (2012)Google Scholar
- 17.Kuhn, D.R., Higdon, J.M., Lawrence, J.F., Kacker, R.N., Lei, Y.: Combinatorial methods for event sequence testing. CrossTalk: J. Defense Software Eng. 25(4), 15–18 (2012)Google Scholar
- 18.Kuhn, D.R., Higdon, J.M., Lawrence, J.F., Kacker, R.N., Lei, Y.: Combinatorial methods for event sequence testing. In: IEEE Fifth International Conference on Software Testing, Verification and Validation (ICST), pp. 601–609 (2012)Google Scholar
- 20.Margalit, O.: Better bounds for event sequence testing. In: The 2nd International Workshop on Combinatorial Testing (IWCT 2013), pp. 281–284 (2013)Google Scholar
- 25.Spencer, J.: Minimal scrambling sets of simple orders. Acta Math. Acad. Sci. Hungar. 22, 349–353 (1971/72)Google Scholar