Subexponential Algorithms for Rectilinear Steiner Tree and Arborescence Problems *

Fedor Fomin, Sudeshna Kolay, Daniel Lokshtanov, Fahad Panolan, Saket Saurabh
unpublished
A rectilinear Steiner tree for a set T of points in the plane is a tree which connects T using horizontal and vertical lines. In the Rectilinear Steiner Tree problem, input is a set T of n points in the Euclidean plane (R 2) and the goal is to find an rectilinear Steiner tree for T of smallest possible total length. A rectilinear Steiner arborecence for a set T of points and root r ∈ T is a rectilinear Steiner tree S for T such that the path in S from r to any point t ∈ T is a shortest path. In
more » ... the Rectilinear Steiner Arborescense problem the input is a set T of n points in R 2 , and a root r ∈ T , the task is to find an rectilinear Steiner arborescence for T , rooted at r of smallest possible total length. In this paper, we give the first subexponential time algorithms for both problems. Our algorithms are deterministic and run in 2 O(√ n log n) time. 1998 ACM Subject Classification F.2 Analysis of Algorithms and Problem Complexity.
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