An algorithm for locating short circuits among N signal paths using K-port parallel short detector

To locate short circuits on a printed circuit board, a K-port parallel short detector can test K signal paths simultaneously. If the total number of signal paths N on a printed circuit board is larger than K, then we need to divide the testing process into multiple stages such that at most R signal paths are tested in each stage. In this paper, we design a parallel algorithm to locate all the short circuits among the N signal paths on a printed circuit board using a K-port parallel short detector where K<N. This algorithm consists of three main steps: (1) it partitions the set of signal paths {1,2,...,N} into disjoint sets S _i´s such that S_i contains at most K signal paths, and then it bisects S_i into two disjoint sets T_2i-1 and T_2i, (2) it locates all the short circuits in S_i for all i, and (3) it locates all the short circuits between S_i and S_j for all i≠j by testing T_2i-1 against T_2j-1, T_2i-1 against T_2j, T_2i against T_2j-1, and T _2i against T_2j