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

Gene Eu Jan, Ki-Yin Chang, Su Gao, Ian Parberry
2005 ACM Transactions on Design Automation of Electronic Systems  
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
more » ... le-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% compared to those in the rectilinear router.
doi:10.1145/1044111.1044118 fatcat:g7eufvnaafc3tnlv7izg4i6jva