New Algorithms and Bounds for Multilayer Channel Routing
Brady, Martin Lee
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Permalink
https://hdl.handle.net/2142/69358
Description
Title
New Algorithms and Bounds for Multilayer Channel Routing
Author(s)
Brady, Martin Lee
Issue Date
1987
Department of Study
Electrical Engineering
Discipline
Electrical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Abstract
This thesis studies the multilayer channel routing problem (CRP). New algorithms are presented in which the number of layers is a parameter of the problem, and the area of the solution improves as the number of layers is increased.
First, the nonadjacent overlap model, in which wires are allowed to overlap, but not in consecutive layers, is considered. A solution is presented which uses at most three tracks over the lower bound of $\left\lceil{d\over\lceil L/2\rceil}\right\rceil.$ We generalize this algorithm to the K-separated overlap model, in which overlapping wires must be at least K layers apart.
Next, the arbitrary overlap model, in which wire overlap is unrestricted, is considered. We give a multiterminal net algorithm which uses only ${d\over L-2} + O (\sqrt {d/L})$ tracks. For the restricted case of two-terminal nets the bound is improved to ${d\over L-1} + O (\sqrt {d/L}),$ within $O(\sqrt {d/L})$ tracks of the $d\over L-1$ lower bound. For a slight restriction of the model in which only $L-1$ wires are allowed to overlap horizontally, the lower bound is improved to ${d\over L-1}$ + $\Omega ({\rm log}\ d/L).$ Moreover, this general strategy yields algorithms which achieve or improve upon the best known upper bounds for many previously studied models, including the Manhattan and knock-knee models, and thus represents a unified approach to the channel routing problem.
Finally, the stacked pins channel routing problem (SCRP), in which each terminal is allowed to contain up to p different nets is studied. New lower bounds for broad classes of stacked pin routing models are proven, and it is shown that the K -separated overlap algorithm can be extended to routing the SCRP with arbitrary overlap.
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