Via design rule consideration in multilayer maze routing algorithms

Maze routing algorithms are widely used for finding an optimal path in detailed routing for very large scale integration, printed circuit board and multichip modules. In this paper, we show that finding an optimal route of a two-pin net in a multilayer routing environment under practical via design rules can be surprisingly difficult. A straightforward extension to the maze routing algorithm that disallows via-rule incorrect routes may either cause a suboptimal route to be found, or more seriously, cause the failure to find any route even if one exists. We present a refined heuristic to this problem by embedding the distance to the most recently placed via in an extended connection graph so that the maze routing algorithm has a higher chance of finding a via-rule correct optimum path in the extended connection graph. We further present efficient data-structures to implement the maze routing algorithm without the need to preconstruct the extended connection graph. Experimental results confirmed the usefulness of our algorithm and its applicability to a wide range of CMOS technologies.