Obstacle-Avoiding Rectilinear Steiner Tree Construction Based on Spanning Graphs

Abstract

Given a set of pins and a set of obstacles on a plane, an obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) connects these pins, possibly through some additional points (called the Steiner points), and avoids running through any obstacle to construct a tree with a minimal total wirelength. The OARSMT problem becomes more important than ever for modern nanometer IC designs which need to consider numerous routing obstacles incurred from power networks, prerouted nets, IP blocks, feature patterns for manufacturability improvement, antenna jumpers for reliability enhancement, etc. Consequently, the OARSMT problem has received dramatically increasing attention recently. Nevertheless, considering obstacles significantly increases the problem complexity, and thus, most previous works suffer from either poor quality or expensive running time. Based on the obstacle-avoiding spanning graph, this paper presents an efficient algorithm with some theoretical optimality guarantees for the OARSMT construction. Unlike previous heuristics, our algorithm guarantees to find an optimal OARSMT for any two-pin net and many higher pin nets. Extensive experiments show that our algorithm results in significantly shorter wirelengths than all state-of-the-art works.

FOARS: FLUTE Based Obstacle-Avoiding Rectilinear Steiner Tree Construction

“…FOARS has a run time complexity of O(n log n). Our experimental results indicate that it outperforms Lin et al [2] by 2.3% in wirelength. FOARS also has 20% faster run time as compared with Long et al [3], which is the fastest solution till date.…”

“…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

“…Based on our understanding of their algorithm, its time complexity is at least O(n 2 ). In fact, it was mentioned that the worst case time complexity of the algorithm of Shen et al is Ω(n 2 log n) [16]. The algorithm of Lin et al produces Steiner trees with comparable quality as our approach, but their algorithm is more expensive (O(n 3 )).…”

“…The OARSMT construction algorithms can be generalized to handle these constraints. For instance, in congestion-driven routing, overcongested regions can be modeled as obstacles [16]. On an obstacle-free routing plane, the OARSMT problem degenerates to the RSMT problem, which has been proven to be NP complete [4].…”