Optimal Bipartite Locating Arrays For At Most Two Faults

Locating arrays are of interest in generating software test suites to cover all t-way component interactions and locate interaction faults in component-based systems.But in the test of radar and jammer,it is a waste of talent to use locating arrays to locate all interaction faults because the interactions within the group are of little sense.Bipartite locating arrays are used to save time and cost of tests.In this paper,we mainly studies bipartite locating arrays for at most faults.Firstly,we establish a lower bound on the size of it,and make the lower bound as the optimal criterion.Then prove that optimal bipartite locating arrays meeting this bound can be equivalently characterized in terms of bipartite orthogonal arrays with "triangle-free" and "quadrangle-free" properties.Then two construction methods to satisfy the prescribed properties are given,namely,the weighted method and the direct construction of the difference matrix.At last,two infinite serie of optimal bipartite locating arrays are then obtained,where a group only has two factors and the number of factors to strength is greater than 1.