**Jose Torres-Jimenez
**

*CINVESTAV-Research 3C, Mexico*

**Title:**

A survey of Covering Arrays

**Abstract:
**A covering arrays denoted by

*CA(N; t, k, v)*is a matrix of

*N*rows and

*k*columns, where each element of the matrix take values from

*{0,1,…,v-1}*; and the matrix satisfies that each subset of

*t*columns contains at least once each combination of

*v*.

^{t}The problem of constructing optimal covering arrays (

*CA*) is a hard combinatorial optimization problem. An optimal

*CA*has the minimum number of rows (

*N*) given

*t*,

*k*, and

*v*.

The covering arrays were used successfully in many areas when it is desired to minimize the number of experiments (

*N*) to obtain some result, controlling some variables (

*k*); for instance they were used in drug screening, agriculture planning, and bioinformatics.

The area in which

*CA*were successfully used extensively is software testing, in software testing the CA were used to construct functional test suites of minimal size.

In this talk a survey of parallel and sequential methods to construct

*CA*will be given. The overview covers

*algebraic*,

*greedy*,

*metaheuristic,*

*exact*, and

*transforming*methods to obtain

*CA*.

The talk will be concluded presenting impressive results of using parallel computing to construct thousands of improved

*CA*.

**Short Bio:**

Dr. Jose Torres-Jimenez is a researcher at CINVESTAV-Tamaulipas (a leader research institution in Mexico). He has: coauthored 5 books; written more than sixty refereed papers; formed more than 60 professionals at graduate level; and developed many projects for the industry. His working on covering arrays starts ten years ago. Dr. Torres-Jimenez is well known for his original developments to construct best-known covering arrays. His homepage is http://www.tamps.cinvestav.mx/~jtj, and his email is: jtj@cinvestav.mx

**Website:**

http://www.tamps.cinvestav.mx/~jtj