Shortest path search using tiles and piecewise linear costpropagation

In this paper we propose a new algorithm for finding shortest paths in a tile connection graph. This algorithm uses an exact piecewise linear cost model to guide our search of the compact tile graph. Unlike previous tile search algorithms, this algorithm always rinds a shortest path. Unlike the grid graph algorithms (which do find shortest paths), this algorithm searches the tile graph which is much smaller than the grid graph. The efficiency of our new approach is confirmed by our experiments comparing our new algorithm with the grid graph algorithms.

[1]  Nils J. Nilsson,et al.  Principles of Artificial Intelligence , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  John K. Ousterhout,et al.  Corner Stitching: A Data-Structuring Technique for VLSI Layout Tools , 1984, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[3]  Jason Cong,et al.  An implicit connection graph maze routing algorithm for ECO routing , 1999, 1999 IEEE/ACM International Conference on Computer-Aided Design. Digest of Technical Papers (Cat. No.99CH37051).

[4]  Dave Hightower.  A solution to line-routing problems on the continuous plane , 1969, DAC '69.

[5]  Chak-Kuen Wong,et al.  Rectilinear Shortest Paths and Minimum Spanning Trees in the Presence of Rectilinear Obstacles , 1987, IEEE Transactions on Computers.

[6]  Kenneth L. Clarkson,et al.  Rectilinear shortest paths through polygonal obstacles in O(n(logn)2) time , 1987, SCG '87.

[7]  Walter S. Scott,et al.  An interactive maze router with hints , 1988, 25th ACM/IEEE, Design Automation Conference.Proceedings 1988..

[8]  Alfred V. Aho,et al.  Data Structures and Algorithms , 1983 .

[9]  David G. Kirkpatrick,et al.  A compact piecewise-linear voronoi diagram for convex sites in the plane , 1996, Discret. Comput. Geom..

[10]  Jürgen Sellen,et al.  Direction weighted shortest path planning , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[11]  C. Y. Lee.  An Algorithm for Path Connections and Its Applications , 1961, IRE Trans. Electron. Comput..

[12]  Carl Sechen,et al.  Chip-level area routing , 1998, ISPD '98.

[13]  Frank O. Hadlock,et al.  A shortest path algorithm for grid graphs , 1977, Networks.

[14]  Alessandro De Gloria,et al.  A Tile-Expansion Router , 1987, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[15]  S. Sitharama Iyengar,et al.  Finding obstacle-avoiding shortest paths using implicit connection graphs , 1996, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[16]  Chia-Chun Tsai,et al.  An H-V alternating router , 1992, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..