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.
KeywordsMinimum Span Tree Steiner Tree Short Path Tree Safe Move Rectilinear Distance
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