Abstract
The rectilinear/octilinear Steiner problem is the problem of connecting a set of terminals $Z$ using orthogonal and diagonal edges with minimum length. This problem has many applications, such as the EDA, VLSI circuit design, fault-tolerant routing in mesh-based broadcast, and Printed Circuit Board (PCB). This paper proposes an obstacle-avoiding 4/8/10/26-directional heuristic algorithm for this problem based on the Areibi’s concept, Higher Geometry Maze Routing, and Sollin’s minimal spanning tree algorithm. The major contributions of this paper are (1) our work is the first report for the octilinear SMTs in the multidimensional environments, (2) we provide an optimal point-to-point routing without any refinement, and (3) the proposed algorithm has higher adaptability to deal with any irregular environment, and can be extended to the $\lambda $ -geometry without any extra work, where $\lambda =2$ , 4, 8 and $\infty $ corresponding to rectilinear, 45°, 22.5° and Euclidean geometries respectively.
Highlights
Routing plays an important role in many applications, such as the Electronic Design Automation (EDA), Very Large Scale Integrated (VLSI) circuit design (X Initiative), fault-tolerant routing in mesh-based broadcast [1], [2], decision systems[3], and Printed Circuit Board (PCB) [4], [5]
Lin et al [24] proposed an obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) construction algorithm that achieves an optimal solution for two-pin net
The results clearly show that our approaches outperform the Connection Graph (CG)/Delaunay Triangulation (DT) based approaches in many cases, since the proposed algorithms seek the shortest path in the free space instead of the path connected from the source, corners of obstacles to the destination
Summary
Routing plays an important role in many applications, such as the Electronic Design Automation (EDA), Very Large Scale Integrated (VLSI) circuit design (X Initiative), fault-tolerant routing in mesh-based broadcast [1], [2], decision systems[3], and Printed Circuit Board (PCB) [4], [5]. Lin et al [24] proposed an obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) construction algorithm that achieves an optimal solution for two-pin net. Their approach guarantees to provide a rectilinear shortest path between any two pins. The main contributions of this paper are listed as follows: (1) the proposed method has high flexibility and ability to handle arbitrary blockages, (2) this method produces optimal point-to-point paths both in 2D planes and 3D volumes without local refinement This quality obviously outperforms other graph based approaches in wire length in multidimensional volumes, and (3) we demonstrate that the Steiner ratio of our algorithms is 1.25. The total time complexity of this algorithm is O(N 2+ Np2 log2p)
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