Finding Minimum Locating Arrays Using a CSP Solver

Abstract

Combinatorial interaction testing is an efficient software testing strategy. If all interactions among test parameters or factors needed to be covered, the size of a required test suite would be prohibitively large. In contrast, this strategy only requires covering $t$-wise interactions where $t$ is typically very small. As a result, it becomes possible to significantly reduce test suite size. Locating arrays aim to enhance the ability of combinatorial interaction testing. In particular, $(\overline{1}, t)$-locating arrays can not only execute all $t$-way interactions but also identify, if any, which of the interactions causes a failure. In spite of this useful property, there is only limited research either on how to generate locating arrays or on their minimum sizes. In this paper, we propose an approach to generating minimum locating arrays. In the approach, the problem of finding a locating array consisting of $N$ tests is represented as a Constraint Satisfaction Problem (CSP) instance, which is in turn solved by a modern CSP solver. The results of using the proposed approach reveal many $(\overline{1}, t)$-locating arrays that are smallest known so far. In addition, some of these arrays are proved to be minimum.