The split k-layer (k ≥ 2) circular topological via minimization (k-CTVM) problem is reconsidered here. The problem is finding a topological routing of the n nets, using k available layers, such that the total number of vias is minimized. The optimal solution of this problem is solved in O(n2k+1) time. However, such an algorithm is inefficient even for n ≥ 8 and k ≥ 2. A heuristic algorithm with complexity of O(k n4) is presented. When the experimental results of this algorithm and that of an exhaustive algorithm are compared, the same number of optimal solutions is obtained from this heuristic algorithm for all permutations of 1) n = 8 with k = 2 or 3, and 2) n = 10 with k = 3. For other cases, the number of optimal solutions from this algorithm depends on the permutations been selected; and this number, in general, will increase as k increases.
