Journal ArticleDOI
A Linear-Time Routing Algorithm for Convex Grids
TLDR
An efficient algorithm is described which necessarily finds a routing in a given grid whenever it exists, and works for a rather large class of grids, called convex grids, including the grids of rectangular, T-, L-, or X-shape boundaries.Abstract:
In this paper, we consider the channel routing problem involving two-terminal nets on rectilinear grids. An efficient algorithm is described which necessarily finds a routing in a given grid whenever it exists. The algorithm is not a heuristic but an exact one, and works for a rather large class of grids, called convex grids, including the grids of rectangular, T-, L-, or X-shape boundaries. Both the running time and required space are linear in the number of vertices of a grid.read more
Citations
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Journal ArticleDOI
Recent advances in VLSI layout
Ernest S. Kuh,T. Ohtsuki +1 more
TL;DR: The current status of VLSI layout and directions for future research are addressed, and the field of computational geometry and its application to layout-in particular, to gridless routing and compaction-are reviewed, and layout engines are considered.
Journal ArticleDOI
Global wire routing in two-dimensional arrays
Richard M. Karp,Frank Thomson Leighton,Ronald L. Rivest,Clark D. Thompson,Umesh Vazirani,Vijay V. Vazirani +5 more
TL;DR: A central result of this paper is a “rounding algorithm” for obtaining integral approximations to solutions of linear equations for matrix A and real vector x.
Journal ArticleDOI
A linear-time algorithm for edge-disjoint paths in planar graphs
Dorothea Wagner,Karsten Weihe +1 more
TL;DR: A new approach to the problem of finding edge-disjoint paths in a planar, undirected graph such that each path connects two specified vertices on the boundary of the graph is introduced, which results in anO(n) algorithm.
Book ChapterDOI
A Linear-Time Algorithm for Edge-Disjoint Paths in Planar Graphs
Dorothea Wagner,Karsten Weihe +1 more
TL;DR: A new approach to the problem of finding edge-disjoint paths in a planar, undirected graph with “classical” case where an instance must additionally fulfill the so-called evenness-condition is introduced.
Journal ArticleDOI
Algorithms for routing in planar graphs
Michael Becker,Kurt Mehlhorn +1 more
TL;DR: It is shown that one can decide in time O(bn) whether a half-even problem is solvable and that a solution can be constructed inTime O(n2), where n=¦V¦ and b is the number of vertices on the boundary of the infinite face.
References
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Proceedings ArticleDOI
A “DOGLEG” channel router
TL;DR: The routing algorithm presented here was developed as part of LTX, a computer-aided design system for integrated circuit layout and was implemented on an HP-2100 minicomputer.
Journal ArticleDOI
Disjoint paths in a rectilinear grid
TL;DR: A good characterization and a good algorithm are given for a special case of the integral multicommodity flow problem when the graph is defined by a rectangle on a rectilinear grid.
Book ChapterDOI
Provably Good Channel Routing Algorithms
TL;DR: Three new two-layer channel routing algorithms are presented that are provably good in that they never require more than 2d-1 horizontal tracks where d is the channel density, when each net connects just two terminals.
Proceedings ArticleDOI
Optimal wiring between rectangles
TL;DR: Although the theoretical model implies that there can be great gains for the two-layer strategy, even in cases where no crossovers are required, when the typical design rules for laying out VLSI circuits are considered, there is no substantial advantage to the twolayer approach over the one-layer approach.
Book ChapterDOI
New Lower Bounds for Channel Width
Donna J. Brown,Ronald L. Rivest +1 more
TL;DR: A simple yet effective technique for calculating a lower bound on the number of tracks required to solve a given channel-routing problem with n two-terminal nets that begin and end in different columns.