NDLI: A Provably Good Algorithm for the Two Module Routing Problem

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Baker, Brenda S.
Copyright Year	1986
Abstract	In the MeadConway design methodology for LSI, modules are designed and then connected by wires to form larger modules in a hierarchical fashion. It would be helpful to have a design aid that would do the routing automatically and be guaranteed of coming within some fixed percentage of the size of an optimal routing. With this goal in mind, we investigate the problem of routing two-terminal nets between two modules of the same width but possibly different heights, assuming that the sides are aligned vertically. The terminals may lie on any of the sides of either module. Wires must be routed according to the Manhattan reserved-layer model, in which all wires must lie on a rectilinear grid, and wires running the same direction must be separated by at least unit distance. Finding an optimal routing for this problem is NP-hard, where the measure of performance is the perimeter of the bounding box around the whole routing region. We describe an algorithm whose worst-case performance is asymptotically at most 19/10 times that of an optimal routing. The algorithm runs in $O(n\log n)$ time, where n is the number of nets.One of the problems encountered in routing is how to evaluate a routing when the optimal routing is not available for comparison. The techniques given here can be used to calculate lower bounds on the size of an optimal routing. Thus, these techniques may be useful in evaluating routings produced by methods other than the algorithm in this paper.
Starting Page	162
Ending Page	188
Page Count	27
File Format	PDF
ISSN	00975397
DOI	10.1137/0215012
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	1
Volume Number	15
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-02
Access Restriction	Subscribed
Subject Keyword	channel routing worst-case performance bound NP-hard wire routing
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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