Applications of algebraic combinatorics to design theory and extremal set-partition theory

对电路、软件和网络进行彻底的测试至关重要，但往往被忽视，因为它可能既复杂又耗时。 研究人员试图找到测试方案，以减少测试系统所需的工作量，同时仍然有一组严格的测试。一种这样的方案是由称为覆盖阵列的设计确定的。覆盖数组描述了一种完全测试系统中每对参数的方案，而不是完全测试系统中所有可能的参数集。这导致测试既有效又高效。对这种测试方案的进一步改进是仅测试已知相互作用的参数对。由于相互作用的对的集合可以记录在图结构中，这导致了一种细化，称为图上的覆盖数组。

Thorough testing of circuits, software and networks is critical but it is often neglected since it can be complicated and time consuming. Researchers have tried to find testing schemes that would reduce the amount of work required to test a system, while still having a rigorous set of tests. One such scheme is determined by a design called a covering array. A covering array describes a scheme that completely tests every pair of parameters in the system, rather than completely testing all possible sets of parameters in a system. This leads to testing that is both effective and efficient. A further improvement on such a testing scheme is to only test pairs of parameters that are known to interact. Since the set of pairs which interact can be recorded in a graph structure, this leads to a refinement, called a covering array on a graph.