The test suite generation problem: Optimal instances and their implications

  • Authors:
  • Christine T. Cheng

  • Affiliations:
  • Department of Computer Science, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2007

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Abstract

In the test suite generation (TSG) problem for software systems, I is a set of n input parameters where each I@?I has @k(I) data values, and O is a collection of subsets of I where the interactions of the parameters in each O@?O are thought to affect the outcome of the system. A test case for (I,O,@k) is an n-tuple (t"1,t"2,...,t"n) that specifies the value of each input parameter in I. The goal is to generate a smallest-sized test suite (i.e., a set of test cases) that covers all combinations of each O@?O. The decision version of TSG is known to be NP-complete. In this paper, we present new families of (I,O,@k) for which optimal test suites can be constructed efficiently. They differ from the ones already known by the way we characterize (I,O) and @k. We then use these instances to generate test suites for arbitrary software systems. When each O@?O has |O|=2, the sizes of the test suite are guaranteed to be at most @?log"2n@?xOPT, matching the current best bound for this problem. Our constructions utilize the structure of (I,O) and @k; consequently, the less ''complex''(I,O) and @k are, the better are the bounds on the sizes of the test suites.