Improving IPOG's vertical growth based on a graph coloring scheme

We show that the vertical growth phase of IPOG is optimal for t-way test generation when t = 2, but it is no longer optimal when t is greater than 2. We present an improvement that reduces the number of tests generated during vertical growth. The vertical growth problem is modeled as a classical NP-hard problem called “Minimum Vertex Coloring”. We adopted a greedy coloring algorithm to determine the order in which missing tuples are covered during vertical growth. We implemented a revised IPOG algorithm incorporating this improvement. The experimental results show that compared with the original IPOG algorithm, which uses an arbitrary order to cover missing tuples during vertical growth, the revised IPOG algorithm reduces the number of tests for many real-life systems.

[1]  Angelo Gargantini,et al.  T‐wise combinatorial interaction test suites construction based on coverage inheritance , 2012, Softw. Test. Verification Reliab..

[2]  Chung C. Wang,et al.  An Algorithm for the Chromatic Number of a Graph , 1974, JACM.

[3]  K.Z. Zamli,et al.  A strategy for Grid based t-way test data generation , 2008, 2008 First International Conference on Distributed Framework and Applications.

[4]  Maciej M. Syslo.  Sequential coloring versus Welsh-Powell bound , 1989, Discret. Math..

[5]  J. Czerwonka.  Pairwise Testing in the Real World : Practical Extensions to Test-Case Scenarios , 2011 .

[6]  Jeff Yu Lei,et al.  IPOG/IPOG‐D: efficient test generation for multi‐way combinatorial testing , 2008, Softw. Test. Verification Reliab..

[7]  Ludek Kucera,et al.  The Greedy Coloring Is a Bad Probabilistic Algorithm , 1991, J. Algorithms.

[8]  Jeff Yu Lei,et al.  ACTS: A Combinatorial Test Generation Tool , 2013, 2013 IEEE Sixth International Conference on Software Testing, Verification and Validation.

[9]  Jeff Yu Lei,et al.  An Efficient Algorithm for Constraint Handling in Combinatorial Test Generation , 2013, 2013 IEEE Sixth International Conference on Software Testing, Verification and Validation.

[10]  Steven Skiena,et al.  Implementing discrete mathematics - combinatorics and graph theory with Mathematica , 1990 .

[11]  Lucas Rioux-Maldague.  Graph Coloring Algorithms , 2014 .

[12]  Kamal Z. Zamli,et al.  MIPOG - An Efficient t-Way Minimization Strategy for Combinatorial Testing , 2011 .

[13]  Yu Lei,et al.  Refining the In-Parameter-Order Strategy for Constructing Covering Arrays , 2008, Journal of research of the National Institute of Standards and Technology.

[14]  Jeff Yu Lei,et al.  IPOG: A General Strategy for T-Way Software Testing , 2007, 14th Annual IEEE International Conference and Workshops on the Engineering of Computer-Based Systems (ECBS'07).

[15]  Yu Lei,et al.  A Test Generation Strategy for Pairwise Testing , 2002, IEEE Trans. Software Eng..

[16]  D. J. A. Welsh,et al.  An upper bound for the chromatic number of a graph and its application to timetabling problems , 1967, Comput. J..

[17]  Yu Lei,et al.  In-parameter-order: a test generation strategy for pairwise testing , 1998, Proceedings Third IEEE International High-Assurance Systems Engineering Symposium (Cat. No.98EX231).