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VLSI Design
Volume 4, Issue 1, Pages 41-51

An Efficient Algorithm for the Split K-Layer Circular Topological Via Minimization Problem

1Advanced Technology Center, Computer & Communication Research Laboratories, Industrial Technology Research Institute, E000, Bldg. 11, 195 Sec. 4, Chung Hsing Rd, Chutung, Hsinchu 31015, Taiwan
2Institute of Computer Science, National Tsing-Hua University, Hsinchu, Taiwan

Received 18 September 1992; Revised 13 December 1993

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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(kn4) 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.