EBOARST: An Efficient Edge-Based Obstacle-Avoiding Rectilinear Steiner Tree Construction Algorithm

Abstract

Obstacle-avoiding Steiner routing has arisen as a fundamental problem in the physical design of modern VLSI chips. In this paper, we present EBOARST, an efficient four-step algorithm to construct a rectilinear obstacle-avoiding Steiner tree for a given set of pins and a given set of rectilinear obstacles. Our contributions are fourfold. First, we propose a novel algorithm, which generates sparse obstacle-avoiding spanning graphs efficiently. Second, we present a fast algorithm for the minimum terminal spanning tree construction step, which dominates the running time of several existing approaches. Third, we present an edge-based heuristic, which enables us to perform both local and global refinements, leading to Steiner trees with small lengths. Finally, we discuss a refinement technique called segment translation to further enhance the quality of the trees. The time complexity of our algorithm is <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> log <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> ). Experimental results on various benchmarks show that our algorithm achieves 16.56 times speedup on average, while the average length of the resulting obstacle-avoiding rectilinear Steiner trees is only 0.46% larger than the best existing solution.