Complexity issues in VLSI: optimal layouts for the shuffle-exchange graph and other networks
Complexity issues in VLSI: optimal layouts for the shuffle-exchange graph and other networks
Three dimensional circuit layouts
SIAM Journal on Computing
An approximation algorithm for Manhattan routing
Advances in computing research, vol. 2
DAC '91 Proceedings of the 28th ACM/IEEE Design Automation Conference
Channel routing of multiterminal nets
Journal of the ACM (JACM)
New algorithmic aspects of the Local Lemma with applications to routing and partitioning
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Three-Dimensional VLSI: a case study
Journal of the ACM (JACM)
Node-Disjoint Paths on the Mesh and a New Trade-Off in VLSI Layout
SIAM Journal on Computing
3-Dimensional Single Active Layer Routing
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
DAC '76 Proceedings of the 13th Design Automation Conference
Wire routing by optimizing channel assignment within large apertures
DAC '71 Proceedings of the 8th Design Automation Workshop
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Consider a planar grid of size w × n. The vertices of the grid are called terminals and pairwise disjoint sets of terminals are called nets. We aim at routing all nets in a cubic grid (above the original grid holding the terminals) in a vertex-disjoint way. However, to ensure solvability, it is allowed to extend the length and the width of the original grid to w′ = sw and n′ = sn by introducing s - 1 pieces of empty rows and columns between every two consecutive rows and columns containing the terminals. Hence the routing is to be realized in a cubic grid of size (s ċ n) × (s ċ w) × h. The objective is to minimize the height h. It is easy to show that the required height can be as large as h = Ω(max(n, w)) in the worst case. In this paper we show that if s ≥ 2 then a routing with height h = 6 max(n, w) can always be found in polynomial time. Furthermore, the constant factor '6' can be improved either by increasing the value of s or by limiting the number of terminals in a net. Possible trade-offs between s and h are discussed and the various constructions presented are compared by measuring the volumes of the routings obtained.