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<p><b>Abstract</b>—The comparison of partition and random sampling methods for software testing has received considerable attention in the literature. A standard criterion for comparisons between random and partition testing based on their expected efficacy in program debugging is the probability of detecting at least one failure causing input in the program's domain. We investigate the relative effectiveness of partition testing versus random testing through the powerful mathematical technique of <it>majorization</it>, which was introduced by Hardy et al. The tools of <it>majorization</it> and the concepts of Schur (convex and concave) functions enable us to derive general conditions under which partition testing is superior to random testing and, consequently, to give further insights into the value of partition testing strategies.</p>
Partition testing, random testing, software debugging, majorization, Schur functions.

H. Singh, P. J. Boland and B. Cukic, "Comparing Partition and Random Testing via Majorization and Schur Functions," in IEEE Transactions on Software Engineering, vol. 29, no. , pp. 88-94, 2003.
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