# Generating a Covering Array Matrix with Simulated Annealing

I've been reading the following paper to understand how I can develop a non deterministic algorithm for test cases generation https://www.researchgate.net/publication/293043297_A_two-stage_algorithm_for_combinatorial_testing

I understand that he is using a two stage solution, having a greedy algorithm as a solution for the first stage. I'm struggling to understand the steps of the first stage and the algorithm itself, specifically in the section 3.1, for which I have the following doubts:

1. It mentions that it receives as an input a CA of size N*K-1, but isn't the value N determined by the algorithm? Maybe an example of the inputs would clarify it.In section 3.3 though, from the step 1 and 2, I understand that the inputs have fixed values for N and if we don't have those values, then a different solution should be applied.

2. I'm not very sure how to interpret "free cells". Its just new empty slots that will have a generated random number?

3. It would be easier to have instructions and a more detailed algorithm specification. However, I'm also failing to understand the pseudo code:

From the pseudo code, I'm not sure whats the M value (I don't think its mentioned), also the meaning of the +∞ symbol and also I'm not sure how he can compute the missing tuples. Perhaps I don't have enough knowledge or I'm not inferring correctly the instructions in the description and the algorithm itself. I'm looking for someone that can help me understand these particular points. (I can't find any contact email from the author).

• I'm not sure we can help you read the paper – perhaps ask your advisor. To answer some of your questions: $N,M$ are inputs to the algorithm; free cells are probably cells whose values hasn't been determined yet. As to a more detailed algorithm specification, that's your task – I don't think anybody here is prepared to program the algorithm for you. – Yuval Filmus Sep 4 '17 at 18:18
• my problem is that I don't have an advisor, this is just me investigating... do you think it would be a good idea to hire a tutor for this? – s0ren1 Sep 4 '17 at 19:03