Constant Row Maximizing Problem for Covering Arrays

A Covering Array denoted by CA(N; t,k,¿) is a matrix of size N × k, where each tuple of t columns has at least one time each of the v^t combinations of symbols. The C As are combinatorial objects used for software testing and design of experiments in: biology, agriculture, medicine, etc. CAs can be constructed using heuristic algorithms, greedy search and algebraic procedures. The Hartman Style Rising Procedures (HSRP) are algebraic procedures to construct large C As. These procedures create large CAs using small CAs. If the small C As have many constant rows, the HSRP provides better large CAs. In this paper we present the constant Row Maximizing Problem (CMRP) for CAs. We propose 4 distinct models to maximize the number of constant rows in a CA. The models were tested with binary and senary CAs and we improved some upper bounds.