1 Search Results for "Fielbaum, Andrés"


Document
Track A: Algorithms, Complexity and Games
A Water-Filling Primal-Dual Algorithm for Approximating Non-Linear Covering Problems

Authors: Andrés Fielbaum, Ignacio Morales, and José Verschae

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)


Abstract
Obtaining strong linear relaxations of capacitated covering problems constitute a significant technical challenge even for simple settings. For one of the most basic cases, the Knapsack-Cover (Min-Knapsack) problem, the relaxation based on knapsack-cover inequalities has an integrality gap of 2. These inequalities are exploited in more general problems, many of which admit primal-dual approximation algorithms. Inspired by problems from power and transport systems, we introduce a general setting in which items can be taken fractionally to cover a given demand. The cost incurred by an item is given by an arbitrary non-decreasing function of the chosen fraction. We generalize the knapsack-cover inequalities to this setting an use them to obtain a (2+ε)-approximate primal-dual algorithm. Our procedure has a natural interpretation as a bucket-filling algorithm which effectively overcomes the difficulties implied by having different slopes in the cost functions. More precisely, when some superior segment of an item presents a low slope, it helps to increase the priority of inferior segments. We also present a rounding algorithm with an approximation guarantee of 2. We generalize our algorithm to the Unsplittable Flow-Cover problem on a line, also for the setting of fractional items with non-linear costs. For this problem we obtain a (4+ε)-approximation algorithm in polynomial time, almost matching the 4-approximation algorithm known for the classical setting.

Cite as

Andrés Fielbaum, Ignacio Morales, and José Verschae. A Water-Filling Primal-Dual Algorithm for Approximating Non-Linear Covering Problems. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 46:1-46:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Copy BibTex To Clipboard

@InProceedings{fielbaum_et_al:LIPIcs.ICALP.2020.46,
  author =	{Fielbaum, Andr\'{e}s and Morales, Ignacio and Verschae, Jos\'{e}},
  title =	{{A Water-Filling Primal-Dual Algorithm for Approximating Non-Linear Covering Problems}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{46:1--46:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.46},
  URN =		{urn:nbn:de:0030-drops-124531},
  doi =		{10.4230/LIPIcs.ICALP.2020.46},
  annote =	{Keywords: Knapsack-Cover Inequalities, Non-Linear Knapsack-Cover, Primal-Dual, Water-Filling Algorithm}
}
  • Refine by Author
  • 1 Fielbaum, Andrés
  • 1 Morales, Ignacio
  • 1 Verschae, José

  • Refine by Classification
  • 1 Mathematics of computing → Discrete optimization
  • 1 Mathematics of computing → Linear programming
  • 1 Theory of computation → Packing and covering problems

  • Refine by Keyword
  • 1 Knapsack-Cover Inequalities
  • 1 Non-Linear Knapsack-Cover
  • 1 Primal-Dual
  • 1 Water-Filling Algorithm

  • Refine by Type
  • 1 document

  • Refine by Publication Year
  • 1 2020

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