Institut für Informatik

Technical Report No. 19, March 1990 - Abstract

Peter Widmayer:
On Shortest Paths in VLSI design

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In physical VLSI design, network design (wiring) is the most time consuming phase. For solving global wiring problems, we propose to first compute form the layout geometry a graph that preserves all shortest paths between pairs of relevant points, and then to operate on that graph for computing shortest paths, Steiner minimal tree approximations, or the like. For a set of points and a set of simple orthogonal polygons as obstacles in the plane, with n input points (polygon corner or other) altogether, we show how a shortest paths preserving graph of size O(n*log n) can be computed in time O(n*log n) in the worst case, with space O(n). We illustrate the merits of this approach with a simple example: If the length of a longest edge in the graph is bounded by a polynomial in n, an assumption that is clearly fulfilled for graphs derived from VLSI layout geometries, then a shortest path can be computed in time O(n*log n*log(log n)) in the worst case; this result improves on the known best one of O(n*(log n)^(3/2)).