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Journal Article: “In-Parameter-Order strategies for covering perfect hash families” by MATRIS research group

Michael Wagner and Dimitris E. Simos from the MATRIS research group published an article for the Elsevier Applied Mathematics and Computation Journal.

Generating optimal covering arrays is a very challenging task where asides its theoretical value has huge impact in software testing, when such mathematical structures are translated to software artifacts. In this work, an In-Parameter-Order algorithm for constructing covering perfect hash families with thousands of columns was designed, which can then be mapped back to covering arrays. With this method, several thousand covering arrays were constructed that improve the state of the art.

The rated A article will be published on May 15, 2022.


In-Parameter-Order strategies for covering perfect hash families


Michael Wagner, Charles J. Colbourn and Dimitris E. Simos


Elsevier, Applied Mathematics and Computation, Volume 421


Combinatorial testing makes it possible to test large systems effectively while maintaining certain coverage guarantees. At the same time, the construction of optimized covering arrays (CAs) with a large number of columns is a challenging task. Heuristic and Metaheuristic approaches often become inefficient when applied to large instances, as the computation of the quality for new moves or solutions during the search becomes too slow. Recently, the generation of covering perfect hash families (CPHFs) has led to vast improvements to the state of the art for many different instances of covering arrays. CPHFs can be considered a compact form of a specific family of covering arrays. Their compact representation makes it possible to apply heuristic methods for instances with a much larger number of columns. In this work, we adapt the ideas of the well-known In-Parameter-Order (IPO) strategy for covering array generation to efficiently construct CPHFs, and therefore implicitly covering arrays. We design a way to realize the concept of vertical extension steps in the context of CPHFs and discuss how a horizontal extension can be implemented in an efficient manner. Further, we develop a horizontal extension strategy for CPHFs with subspace restrictions that identifies candidate columns greedily based on conditional expectation. Then using a local optimization strategy, a candidate may be adjoined to the solution or may replace one of the existing columns. An extensive set of computational results yields many significant improvements on the sizes of the smallest known covering arrays.


  • IPO strategy generates Covering Perfect Hash Families efficiently.
  • Fast covering array generation for large scale combinatorial testing.
  • Many improvements to upper bounds on CAN.
  • CPHFs with subspace restrictions lead to many different small CAs.

Link to Science Direct

MATRIS – Mathematics for Testing, Reliability and Information Security Research Group