An O ( n log n ) edge-based algorithm for obstacle-avoiding rectilinear steiner tree construction

Abstract

Obstacle-avoiding Steiner tree construction is a fundamental problem in VLSI physical design. In this paper, we provide a new approach for rectilinear Steiner tree construction in the presence of obstacles. We propose a novel algorithm, which generates sparse obstacle-avoiding spanning graphs efficiently. We design a fast algorithm for the minimum terminal spanning tree construction, which is the bottleneck step of several existing approaches in terms of running time. We adopt an edge-based heuristic, which enables us to perform both local and global refinement, leading to Steiner trees with small lengths. The time complexity of our algorithm is O(nlogn). Hence, our technique is the most efficient one to the best of our knowledge. Experimental results on various benchmarks show that our algorithm achieves 25.8 times speedup on average, while the average length of the resulting obstacle-avoiding rectilinear Steiner trees is only 1.58% larger than the best existing solution.

FOARS: FLUTE Based Obstacle-Avoiding Rectilinear Steiner Tree Construction

“…Routing of multi-terminal nets in the presence of obstacles has become a quintessential part of the design and has been studied by many (e.g., [2][3][4][5][6][7][8][9][10][11][12]). As pointed out by Hwang [13], in the absence of obstacles multi-terminal net routing corresponds to the rectilinear Steiner minimal tree problem which is NPcomplete.…”

“…Both the escape graph and Delaunay triangulation based graph contain O(n 2 ) edges, where n is the total number of pins and obstacle corners. [2,3,5,8,9] are based on various forms of obstacle-avoiding spanning graphs. Shen et al [5] proposed a form of OASG that only contains a linear number of edges which is also adopted in [8].…”

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

“…In this section, we provide the experimental results on several commonly used test cases [8], [10], [24], [28]. We have implemented our algorithm in C++ language and compiled it using gcc 3.4.6.…”

“…Comparison of the quality of the Steiner trees generated by the four algorithms is provided in Table I. Benchmarks IND01∼IND05, RC01∼RC12, RT01∼RT05, and RL01∼RL05 are test cases used in previous works [8], [10], [11], [24]. Benchmarks Adaptec2∼Bigblue4 are based on the placement benchmarks used in ISPD 2005 Placement Contest [28].…”

“…We designed an O(n log n) OARST algorithm recently [24]. In this paper, we extend our preliminary work in several aspects.…”