eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-06-10
39:1
39:15
10.4230/LIPIcs.SoCG.2016.39
article
Subexponential Algorithms for Rectilinear Steiner Tree and Arborescence Problems
Fomin, Fedor
Kolay, Sudeshna
Lokshtanov, Daniel
Panolan, Fahad
Saurabh, Saket
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 in T is a rectilinear Steiner tree S for T such that the path in S from r to any point t in T is a shortest path. In the Rectilinear Steiner Arborescense problem the input is a set T of n points in R^2, and a root r in 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(sqrt{n}log n)} time.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol051-socg2016/LIPIcs.SoCG.2016.39/LIPIcs.SoCG.2016.39.pdf
Rectilinear graphs
Steiner arborescence
parameterized algorithms