Subexponential algorithms for rectilinear Steiner tree and arborescence problems

Fedor Fomin, Sudeshna Kolay, Daniel Lokshtanov, Fahad Panolan, Saket Saurabh

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

Abstract

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.

Original languageEnglish
Title of host publication32nd International Symposium on Computational Geometry, SoCG 2016
EditorsSandor Fekete, Anna Lubiw
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages39.1-39.15
ISBN (Electronic)9783959770095
DOIs
StatePublished - 1 Jun 2016
Externally publishedYes
Event32nd International Symposium on Computational Geometry, SoCG 2016 - Boston, United States
Duration: 14 Jun 201617 Jun 2016

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume51
ISSN (Print)1868-8969

Conference

Conference32nd International Symposium on Computational Geometry, SoCG 2016
Country/TerritoryUnited States
CityBoston
Period14/06/1617/06/16

Keywords

  • Parameterized algorithms
  • Rectilinear graphs
  • Steiner arborescence

ASJC Scopus subject areas

  • Software

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