On rectilinear distance-preserving trees

Given a set of terminals on the plane N=(s,ν₁,...,ν_n,), with a sink terminal s, a Rectilinear Distance-Preserving Tree (RDPT) T(V, E) is defined as a tree rooted at s, connecting all terminals in N. The rectilinear distance between source and sinks in an RDPT is equal to the length that source to sink path. A Min-Cost Rectilinear Distance Preserving Tree (MRDPT) is an RDPT T* such that all other RDPTs T´ connecting s and N have C(T*)⩽C(T´), where C(T) denotes the total length of tree T. MRDPTs minimize the total wire length while maintaining minimal source to sink linear delay, making them suitable for high performance interconnect applications. In this paper we investigate exact algorithms for restricted versions of the problem. These algorithms have O(n²) time complexity. We propose a heuristic algorithm for the general problem where we partition the points into sets of points that we can solve optimally. The results of our algorithms are tested on random point sets and compared our results are compared with Minimum Cost Steiner tree approximations, showing total wire-length comparisons. The results of these comparisons show that the algorithms proposed herein produce promising results