ABSTRACT
The Southeastern Conference on Combinatorics, Graph Theory, and Computing has a long and important history. One of the many strengths of the conference has been its success in bringing together researchers engaged in developing deep and elegant combinatorial theory and researchers developing powerful algorithms with applications to practical problems. This chapter explores one area in which this interplay between theory and application has been fruitful for both. It starts with an anecdote, for which the authors develop a more precise formulation later. Combinatorial testing enables one to determine whether some interaction causes system failure using ‘few’ tests. When one wants to determine which interactions cause system failure, more severe requirements on the combinatorial arrays used for testing must be enforced. It is worthwhile to emphasize the manner in which practical computation on applications problems underpins the need for theory; and the manner in which combinatorial theory supports and improves computation and application.
