TY - GEN

T1 - Subexponential algorithms for rectilinear Steiner tree and arborescence problems

AU - Fomin, Fedor

AU - Kolay, Sudeshna

AU - Lokshtanov, Daniel

AU - Panolan, Fahad

AU - Saurabh, Saket

N1 - Funding Information:
This work was partially supported by the European Research Council (ERC) via grants Rigorous Theory of Preprocessing, reference 267959 and PARAPPROX, reference 306992.
Publisher Copyright:
© Fedor Fomin, Sudeshna Kolay, Daniel Lokshtanov, Fahad Panolan, and Saket Saurabh.

PY - 2016/6/1

Y1 - 2016/6/1

N2 - 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 (ℝ2) 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 the RECTILINEAR STEINER ARBORESCENSE problem the input is a set T of n points in ℝ2, 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 2O(√n log n) time.

AB - 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 (ℝ2) 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 the RECTILINEAR STEINER ARBORESCENSE problem the input is a set T of n points in ℝ2, 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 2O(√n log n) time.

KW - Parameterized algorithms

KW - Rectilinear graphs

KW - Steiner arborescence

UR - http://www.scopus.com/inward/record.url?scp=84976866493&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.SoCG.2016.39

DO - 10.4230/LIPIcs.SoCG.2016.39

M3 - Conference contribution

AN - SCOPUS:84976866493

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 39.1-39.15

BT - 32nd International Symposium on Computational Geometry, SoCG 2016

A2 - Fekete, Sandor

A2 - Lubiw, Anna

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 32nd International Symposium on Computational Geometry, SoCG 2016

Y2 - 14 June 2016 through 17 June 2016

ER -