Given a set of terminals on the plane N={s,ν1,…,νn}, with a source terminal s, a
Rectilinear Distance-Preserving Tree (RDPT) T(V, E) is defined as a tree rooted at s,
connecting all terminals in N. An RDPT has the property that the length of every source
to sink path is equal to the rectilinear distance between that source and sink. A Min-
Cost Rectilinear Distance-Preserving Tree (MRDPT) minimizes the total wire length
while maintaining minimal source to sink linear delay, making it suitable for high
performance interconnect applications.This paper studies problems in the construction of RDPTs, including the following
contributions. A new exact algorithm for a restricted version of the problem in one
quadrant with O(n2) time complexity is proposed. A novel heuristic algorithm, which
uses optimally solvable sub-problems, is proposed for the problem in a single quadrant.
The average and worst-case time complexity for the proposed heuristic algorithm are O(n3/2) and O(n3), respectively. A 2-approximation of the quadrant merging problem is proposed. The proposed algorithm has time complexity O(α2T(n)+α3) for any constant
α > 1, where T(n) is the time complexity of the solution of the RDPT problem on one
quadrant. This result improves over the best previous quadrant merging solution which
has O(n2T(n)+n3) time complexity.We test our algorithms on randomly uniform point sets and compare our heuristic
RDPT construction against a Minimum Cost Rectilinear Steiner (MRST) tree
approximation algorithm. Our results show that RDPTs are competitive with Steiner
trees in total wire-length when the number of terminals is less than 32. This result makes
RDPTs suitable for VLSI routing applications. We also compare our algorithm to the
Rao-Shor RDPT approximation algorithm obtaining improvements of up to 10% in
total wirelength. These comparisons show that the algorithms proposed herein produce
promising results.
