2026-09-20T17:22:55Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/69358 2023-07-11 col_2142_5131 col_2142_8888 com_2142_5130 com_2142_8887 com_2142_234

Brady, Martin Lee 2014-12-15T19:05:17Z 2014-12-15T19:05:17Z 10000-01-01 1987 1987 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. Made available in DSpace on 2014-12-15T19:05:17Z (GMT). No. of bitstreams: 1 8721593.pdf: 2867115 bytes, checksum: 31a1c4471383fe221a3177fd4b25c51d (MD5) Previous issue date: 1987 Embargo set by: Seth Robbins for item 69524 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 85 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1987. http://hdl.handle.net/2142/69358 (UMI)AAI8721593 Engineering, Electronics and Electrical New Algorithms and Bounds for Multilayer Channel Routing text Electrical Engineering Electrical Engineering University of Illinois at Urbana-Champaign Dissertation Ph.D.