Given a set of points Pin a 2D plane, the Steiner tree problem seeks a set of additional points Sso that the wirelength of minimum spanning tree (MST) of P ∪ Sis minimum. Additional objectives include performance-related metrics such as radius and delay. The rectilinear version of this problem—rectilinear Steiner tree (RST)–has an important application in VLSI routing and has seen a huge volume of works. This chapter presents sample problems related to the following works:
L-shaped Steiner routing algorithm [Ho et al., 1990]
1-Steiner algorithms by Kahng and Robins [Kahng and Robins, 1992] and by Borah, Owens, and Irwin [Borah et al., 1994]
BPRIM (Bounded Prim) and BRBC (Bounded Radius Bounded Cost) algorithms [Cong et al., 1992]
A-tree algorithm [Cong et al., 1993]
ERT (Elmore Routing Tree) and SERT (Steiner Elmore Routing Tree) algorithms [Boese et al., 1995]
The first two works focus on wirelength minimization, while the last three are delay-oriented works. The first work constructs an MST first and rectilinearize it by transforming the edges in the MST into L-shapes. The second work transforms a given MST into a Steiner tree by adding Steiner points oneby- one. The third work addresses the wirelength and delay (= measured by so called radius) trade-off during rectilinear MST construction. The fourth work builds the minimum-cost rectilinear Steiner arborescence, where the sourcesink path length is the shortest for all sinks. The last work constructs Steiner trees that directly minimize Elmore delay objective.
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