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An approximation algorithm for the maximum leaf spanning arborescence problem

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Matthew Drescher,

Adrian VettaAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 6, Issue 3

Article No.: 46, Pages 1 - 18

https://doi.org/10.1145/1798596.1798599

Published: 02 July 2010 Publication History

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Abstract

We present an O(√opt)-approximation algorithm for the maximum leaf spanning arborescence problem, where opt is the number of leaves in an optimal spanning arborescence. The result is based upon an O(1)-approximation algorithm for a special class of directed graphs called willows. Incorporating the method for willow graphs as a subroutine in a local improvement algorithm gives the bound for general directed graphs.

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Neuwohner M(2024)A -Approximation for the Maximum Leaf Spanning Arborescence Problem in DAGsInteger Programming and Combinatorial Optimization10.1007/978-3-031-59835-7_25(337-350)Online publication date: 3-Jul-2024
https://dl.acm.org/doi/10.1007/978-3-031-59835-7_25
Fellows MKulik ARosamond FShachnai H(2018)Parameterized approximation via fidelity preserving transformationsJournal of Computer and System Sciences10.1016/j.jcss.2017.11.00193(30-40)Online publication date: May-2018
https://doi.org/10.1016/j.jcss.2017.11.001
Gandhi RHajiaghayi MKortsarz GPurohit MSarpatwar K(2018)On maximum leaf trees and connections to connected maximum cut problemsInformation Processing Letters10.1016/j.ipl.2017.06.002129(31-34)Online publication date: Jan-2018
https://doi.org/10.1016/j.ipl.2017.06.002
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Index Terms

An approximation algorithm for the maximum leaf spanning arborescence problem
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Combinatorial algorithms

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cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 6, Issue 3

June 2010

304 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/1798596

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Association for Computing Machinery

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Publication History

Published: 02 July 2010

Accepted: 01 April 2008

Received: 01 August 2007

Published in TALG Volume 6, Issue 3

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Neuwohner M(2024)A -Approximation for the Maximum Leaf Spanning Arborescence Problem in DAGsInteger Programming and Combinatorial Optimization10.1007/978-3-031-59835-7_25(337-350)Online publication date: 3-Jul-2024
https://dl.acm.org/doi/10.1007/978-3-031-59835-7_25
Fellows MKulik ARosamond FShachnai H(2018)Parameterized approximation via fidelity preserving transformationsJournal of Computer and System Sciences10.1016/j.jcss.2017.11.00193(30-40)Online publication date: May-2018
https://doi.org/10.1016/j.jcss.2017.11.001
Gandhi RHajiaghayi MKortsarz GPurohit MSarpatwar K(2018)On maximum leaf trees and connections to connected maximum cut problemsInformation Processing Letters10.1016/j.ipl.2017.06.002129(31-34)Online publication date: Jan-2018
https://doi.org/10.1016/j.ipl.2017.06.002
Solis-Oba RBonsma PLowski S(2017)A 2-Approximation Algorithm for Finding a Spanning Tree with Maximum Number of LeavesAlgorithmica10.1007/s00453-015-0080-077:2(374-388)Online publication date: 1-Feb-2017
https://dl.acm.org/doi/10.1007/s00453-015-0080-0
Binkele-Raible DFernau HFomin FLokshtanov DSaurabh SVillanger Y(2012)Kernel(s) for problems with no kernelACM Transactions on Algorithms10.1145/2344422.23444288:4(1-19)Online publication date: 4-Oct-2012
https://dl.acm.org/doi/10.1145/2344422.2344428
Binkele-Raible DFernau H(2012)An exact exponential-time algorithm for the Directed Maximum Leaf Spanning Tree problemJournal of Discrete Algorithms10.1016/j.jda.2012.03.00615(43-55)Online publication date: 1-Aug-2012
https://dl.acm.org/doi/10.1016/j.jda.2012.03.006
Bonsma P(2012)Max-leaves spanning tree is APX-hard for cubic graphsJournal of Discrete Algorithms10.1016/j.jda.2011.06.00512(14-23)Online publication date: 1-Apr-2012
https://dl.acm.org/doi/10.1016/j.jda.2011.06.005
Fellows MKulik ARosamond FShachnai H(2012)Parameterized approximation via fidelity preserving transformationsProceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I10.1007/978-3-642-31594-7_30(351-362)Online publication date: 9-Jul-2012
https://dl.acm.org/doi/10.1007/978-3-642-31594-7_30
Bonsma PDorn F(2011)Tight bounds and a fast FPT algorithm for directed Max-Leaf Spanning TreeACM Transactions on Algorithms10.1145/2000807.20008127:4(1-19)Online publication date: 28-Sep-2011
https://dl.acm.org/doi/10.1145/2000807.2000812
Bonsma PZickfeld F(2011)A 3/2-Approximation Algorithm for Finding Spanning Trees with Many Leaves in Cubic GraphsSIAM Journal on Discrete Mathematics10.1137/10080125125:4(1652-1666)Online publication date: 1-Dec-2011
https://dl.acm.org/doi/10.1137/100801251
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Tight bounds and a fast FPT algorithm for directed Max-Leaf Spanning Tree

Spanning Directed Trees with Many Leaves

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