Abstract
Covering arrays (CAs) can be used to detect the existence of faulty pairwise interactions between parameters or components in a software system. The generalization considered here applies to the situation in which some input combinations are invalid. In this paper, we study covering arrays avoiding forbidden edges (CAFEs), where certain pairwise interactions are forbidden while all others must be covered. We study the complexity of the problem and give an algorithm for the case of binary alphabets.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Brigham, R.C., Dutton, R.D.: Upper bounds on the edge clique cover number of a graph. Discrete Math. 52, 31–37 (1984)
Brigham, R.C., Dutton, R.D.: A compilation of relations between graph invariants. Supplement I. Networks 21, 421–455 (1991)
Burr, K., Young, W.: Combinatorial test techniques: Table-based automation, test generation, and code coverage. In: Proc. Intl. Conf. on Soft. Test. Anal. and Rev., October 1998, pp. 503–513. ACM, New York (1998)
Cawse, J.N.: Experimental design for combinatorial and high throughput materials development. GE Global Research Technical Report 29, 769–781 (2002)
Cohen, M.B., Dwyer, M.B., Shi, J.: Interaction testing of highly-configurable systems in the presence of constraints. In: International Symposium on Software Testing and Analysis (ISSTA), London, July 2007, pp. 129–139 (2007)
Colbourn, C.J.: Combinatorial aspects of covering arrays. Le Matematiche(Catania) 58, 121–167 (2004)
Colbourn, C.J.: Covering arrays. In: Colbourn and Dinitz [8], pp. 361–364
Colbourn, C.J., Dinitz, J.H. (eds.): Handbook of combinatorial designs, 2nd edn. Discrete Mathematics and its Applications. Chapman & Hall/CRC, Boca Raton (2007)
Dalal, S.R., Karunanithi, A.J.N., Leaton, J.M.L., Patton, G.C.P., Horowitz, B.M.: Model-based testing in practice. In: Proc. Intl. Conf. on Software Engineering (ICSE 1999), pp. 285–294 (1999)
Dunietz, S., Ehrlich, W.K., Szablak, B.D., Mallows, C.L., Iannino, A.: Applying design of experiments to software testing. In: Proc. Intl. Conf. on Software Engineering (ICSE 1997), October 1997, pp. 205–215. IEEE, Los Alamitos (1997)
Erdős, P., Goodman, A.W., Pósa, L.: The representation of a graph by set intersections. Canad. J. Math. 18, 106–112 (1966)
Gargano, L., Körner, J., Vaccaro, U.: Sperner capacities. Graphs Combin. 9, 31–46 (1993)
Gyárfás, A.: A simple lower bound on edge coverings by cliques. Discrete Math. 85, 103–104 (1990)
Kou, L.T., Stockmeyer, L.J., Wong, C.K.: Covering edges by cliques with regard to keyword conflicts and intersection graphs. Comm. ACM 21, 135–139 (1978)
Kuhn, D.R., Reilly, M.: An investigation of the applicability of design of experiments to software testing. In: Proc. 27th Annual NASA Goddard/IEEE Software Engineering Workshop, October 2002, pp. 91–95. IEEE, Los Alamitos (2002)
Kuhn, D.R., Wallace, D.R., Gallo, A.M.: Software fault interactions and implications for software testing. IEEE Trans. Soft. Eng. 30, 418–421 (2004)
Lovász, L.: On covering of graphs. In: Theory of Graphs (Proc. Colloq., Tihany, 1966), pp. 231–236. Academic Press, New York (1968)
Mandl, R.: Orthogonal latin squares: An application of experiment design to compiler testing. Communic. of the ACM 28, 1054–1058 (1985)
Martinez, C., Moura, L., Panario, D., Stevens, B.: Algorithms to locate errors using covering arrays. In: Proc. LATIN 2008 - 8th Latin American Theoretical INformatics conference (April 2008)
Meagher, K., Moura, L., Zekaoui, L.: Mixed covering arrays on graphs. Journal of Combinatorial Designs 15, 393–404 (2007)
Meagher, K., Stevens, B.: Covering arrays on graphs. J. Combin. Theory. Ser. B 95, 134–151 (2005)
Moura, L., Stardom, J., Stevens, B., Williams, A.W.: Covering arrays with mixed alphabet sizes. J. Combin. Des. 11, 413–432 (2003)
Nuutila, E.: Efficient transitive closure computation in large digraphs. Acta Polytechnica Scandinavica, Mathematics and Computing in Engineering Series, Finnish Academy of Technology, vol. 74 (1995)
Seroussi, G., Bshouty, N.H.: Vector sets for exhaustive testing of logic circuits. IEEE Transactions on Information Theory 34, 513–522 (1988)
Shasha, D.E., Kouranov, A.Y., Lejay, L.V., Chou, M.F., Coruzzi, G.M.: Using combinatorial design to study regulation by multiple input signals: A tool for parsimony in the post-genomics era. Plant Physiology 127, 1590–2594 (2001)
Tang, D.T., Chen, C.L.: Iterative exhaustive pattern generation for logic testing. IBM Journal Research and Development 28, 212–219 (1984)
Williams, A.W., Probert, R.L.: A measure for component interaction test coverage. In: Proc. ACS/IEEE Intl. Conf. Comput. Syst. & Applic., pp. 301–311 (2001)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Danziger, P., Mendelsohn, E., Moura, L., Stevens, B. (2008). Covering Arrays Avoiding Forbidden Edges. In: Yang, B., Du, DZ., Wang, C.A. (eds) Combinatorial Optimization and Applications. COCOA 2008. Lecture Notes in Computer Science, vol 5165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85097-7_28
Download citation
DOI: https://doi.org/10.1007/978-3-540-85097-7_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85096-0
Online ISBN: 978-3-540-85097-7
eBook Packages: Computer ScienceComputer Science (R0)