An Improved Augmented Line Segment based Algorithm for the Generation of Rectilinear Steiner Minimum Tree

Abstract

An improved Augmented Line Segment Based (ALSB) algorithm for the construction of Rectilinear Steiner Minimum Tree using augmented line segments is proposed. The proposed algorithm works by incrementally increasing the length of line segments drawn from all the points in four directions. The edges are incrementally added to the tree when two line segments intersect. The reduction in cost is obtained by postponing the addition of the edge into the tree when both the edges (upper and lower Lshaped layouts) are of same length or there is no overlap. The improvement is focused on reduction of the cost of the tree and the number of times the line segments are augmented. Instead of increasing the length of line segments by 1, the line segments length are doubled each time until they cross the intersection point between them. The proposed algorithm reduces the wire length and produces good reduction in the number of times the line segments are incremented. Rectilinear Steiner Minimum Tree has the main application in the global routing phase of VLSI design. The proposed improved ALSB algorithm efficiently constructs RSMT for the set of circuits in IBM benchmark. Keyword:Global routing Rectilinear minimum spanning tree Rectilinear steiner minimum tree VLSI design Copyright © 2017 Institute of Advanced Engineering and Science.All rights reserved. Corresponding Author:Vani V, Department of Information Science and Engineering, Bangalore Institute of Technology, K R Road, V V Puram, Bangalore, Karnatake-560004, India. Email: vanisrin@gmail.com INTRODUCTIONRectilinear Steiner Minimum Tree (RSMT) is the tree that connects the given set of points in a rectilinear fashion using only horizontal and vertical line segments. Few additional points called as Steiner points are added to the tree. Steiner points are added to connect the edges in rectilinear manner and to reduce the total cost of the tree. The rectilinear distance between two points p 1 ={x 1 , y 1 } and p 2 ={x 2 , y 2 } is given by |x 1 -x 2 | + |y 1 -y 2 |. The main application of RSMT is in the global routing phase of the VLSI design. During global routing, the wiring channels (points) that have been placed at particular position using placement algorithm will be connected in rectilinear manner. Figure 1 illustrates the RSMT constructed over the points P 1 to P 8 respectively. It can be identified that all the edges of the RSMT are the part of Hanan Grid. An edge can be either degenerate or nondegenerate. An edge is degenerate, if the two points it connects are in the same x-axis or y-axis. The nondegenerate edge for connecting two points is obtained from the enclosing rectangle and can be either the upper L-Shaped layout or the lower L-shaped layout. The cost or the total length of the RSMT can be reduced by carefully selecting an appropriate layout for each edge that overlaps with the layout of the other edges. For example in the Figure 1, the lower L-shaped layouts are selected for connecting the two edges P 1 -P 2 and P 2 -P 6 as they result in overlap and hence ...

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