A 4-geometry maze router and its application on multiterminal nets

Authors:
Gene Eu Jan;Ki-Yin Chang;Su Gao;Ian Parberry
Affiliations:
National Taipei University, Sun Shia, Taipei;National Taiwan Ocean University, Keelung, Taiwan;University of North Texas, Denton, TX;University of North Texas, Denton, TX
Venue:
ACM Transactions on Design Automation of Electronic Systems (TODAES)
Year:
2005

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Abstract

The maze routing problem is to find an optimal path between a given pair of cells on a grid plane. Lee's algorithm and its variants, probably the most widely used maze routing method, fails to work in the 4-geometry of the grid plane. Our algorithm solves this problem by using a suitable data structure for uniform wave propagation in the 4-geometry, 8-geometry, etc. The algorithm guarantees finding an optimal path if it exists and has linear time and space complexities. Next, to solve the obstacle-avoiding rectilinear and 4-geometry Steiner tree problems, a heuristic algorithm is presented. The algorithm utilizes a cost accumulation scheme based on the maze router to determine the Torricelli vertices (points) for improving the quality of multiterminal nets. Our experimental results show that the algorithm works well in practice. Furthermore, using the 4-geometry router, path lengths can be significantly reduced up to 12&percent; compared to those in the rectilinear router.