1 Search Results for "Torres, Manuel R."

Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2021.24
Fast Approximation Algorithms for Bounded Degree and Crossing Spanning Tree Problems

Authors: Chandra Chekuri, Kent Quanrud, and Manuel R. Torres

Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)

Abstract
We develop fast approximation algorithms for the minimum-cost version of the Bounded-Degree MST problem (BD-MST) and its generalization the Crossing Spanning Tree problem (Crossing-ST). We solve the underlying LP to within a (1+ε) approximation factor in near-linear time via the multiplicative weight update (MWU) technique. This yields, in particular, a near-linear time algorithm that outputs an estimate B such that B ≤ B^* ≤ ⌈(1+ε)B⌉+1 where B^* is the minimum-degree of a spanning tree of a given graph. To round the fractional solution, in our main technical contribution, we describe a fast near-linear time implementation of swap-rounding in the spanning tree polytope of a graph. The fractional solution can also be used to sparsify the input graph that can in turn be used to speed up existing combinatorial algorithms. Together, these ideas lead to significantly faster approximation algorithms than known before for the two problems of interest. In addition, a fast algorithm for swap rounding in the graphic matroid is a generic tool that has other applications, including to TSP and submodular function maximization.
Cite as

Chandra Chekuri, Kent Quanrud, and Manuel R. Torres. Fast Approximation Algorithms for Bounded Degree and Crossing Spanning Tree Problems. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 24:1-24:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{chekuri_et_al:LIPIcs.APPROX/RANDOM.2021.24,
  author =	{Chekuri, Chandra and Quanrud, Kent and Torres, Manuel R.},
  title =	{{Fast Approximation Algorithms for Bounded Degree and Crossing Spanning Tree Problems}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{24:1--24:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.24},
  URN =		{urn:nbn:de:0030-drops-147177},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.24},
  annote =	{Keywords: bounded degree spanning tree, crossing spanning tree, swap rounding, fast approximation algorithms}
}
  • Refine by Author
  • 1 Chekuri, Chandra
  • 1 Quanrud, Kent
  • 1 Torres, Manuel R.

  • Refine by Classification
  • 1 Theory of computation → Approximation algorithms analysis
  • 1 Theory of computation → Graph algorithms analysis

  • Refine by Keyword
  • 1 bounded degree spanning tree
  • 1 crossing spanning tree
  • 1 fast approximation algorithms
  • 1 swap rounding

  • Refine by Type
  • 1 document

  • Refine by Publication Year
  • 1 2021

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact