A practical and efficient approach to the constrained via minimization problem
This paper presents an efficient and practical approach to the Constrained Via Minimization (CVM) problem, which assigns wire segments to the layers, using the minimum number of vias, given a feasible partial routing. The feasible partial routing is first represented by a directed bipartite graph to reflect the mutual constraints. An energy function is then proposed to turn the problem into a cost optimization problem. An efficient heuristic algorithm, combining hill-climbing and simulated annealing, is developed for the cost optimization. The algorithm has the capability to escape from the local minimums and eventually reaches a near-optimal or optimal solution. The proposed method is practical as it can handle many practical constraints such as a multi-way wire split from a single via, and pre-allocation of power nets and terminals. Experimental results show that our proposed method is efficient in handling complex grid-based routing.
constrained via minimization cost optimization heuristic algorithm topological via minimization layer assignment problem