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VLSI Design
Volume 7, Issue 4, Pages 365-383
http://dx.doi.org/10.1155/1998/14757

On Ensuring Multilayer Wirability by Stretching Layouts

1Department of Computer Science, University of California, Santa Barbara, CA 93106, USA
2Computer Science Department, Louisiana State University, Baton Rouge, LA 70803-4020, USA

Received 28 July 1995; Accepted 22 August 1995

Copyright © 1998 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.

Abstract

Every knock-knee layout is four-layer wirable. However, there are knock-knee layouts that cannot be wired in less than four layers. While it is easy to determine whether a knock-knee layout is one-layer wirable or two-layer wirable, the problem of determining three-layer wirability of knock-knee layouts is NP-complete. A knock-knee layout may be stretched vertically (horizontally) by introducing empty rows (columns) so that it can be wired in fewer than four layers. In this paper we discuss two different types of stretching schemes. It is known that under these two stretching schemes, any knock-knee layout is three-layer wirable by stretching it up to (4/3) of the knock-knee layout area (upper bound). We show that there are knock-knee layouts that when stretched and wired in three layers under scheme I (II) require at least 1.2 (1.07563) of the original layout area. Our lower bound for the area increase factor can be used to guide the search for effective stretching-based dynamic programming three-layer wiring algorithms similar to the one presented in [8].