License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2023.104
URN: urn:nbn:de:0030-drops-187570
URL: https://drops.dagstuhl.de/opus/volltexte/2023/18757/
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Zuzic, Goran

A Simple Boosting Framework for Transshipment

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LIPIcs-ESA-2023-104.pdf (0.9 MB)


Abstract

Transshipment is an important generalization of both the shortest path problem and the optimal transport problem. The task asks to route a demand using a flow of minimum cost over (uncapacitated) edges. Transshipment has recently received extensive attention in theoretical computer science as it is the centerpiece of all modern theoretical breakthroughs in parallel and distributed (approximate) shortest-path computation, a classic and well-studied problem.
The key advantage of transshipment over shortest paths is the so-called boosting property: one can often boost a crude approximate solution to a (near-optimal) (1+ε)-approximate solution. However, our understanding of this phenomenon is limited: it is not clear which approximators can be boosted. Moreover, all current boosting frameworks are built with a specific type of approximator in mind and are relatively complicated.
The main takeaway of our paper is conceptual: any black-box oracle that computes an approximate dual solution can be boosted to an (1+ε)-approximator. This decouples and simplifies all known near-optimal (1+ε)-approximate transshipment and shortest paths results: they all (implicitly) construct approximate dual solutions and boost them.
We provide a very simple analysis based on the multiplicative weights framework. Furthermore, to keep the paper completely self-contained, we provide a new (and arguably much simpler) analysis of multiplicative weights that leverages well-known optimization tools to bypass the ad-hoc calculations used in the standard analyses.

BibTeX - Entry

@InProceedings{zuzic:LIPIcs.ESA.2023.104,
  author =	{Zuzic, Goran},
  title =	{{A Simple Boosting Framework for Transshipment}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{104:1--104:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18757},
  URN =		{urn:nbn:de:0030-drops-187570},
  doi =		{10.4230/LIPIcs.ESA.2023.104},
  annote =	{Keywords: mixed continuous-discrete optimization, boosting, multiplicative weights, theoretical computer science, shortest path, parallel algorithms}
}

Keywords: mixed continuous-discrete optimization, boosting, multiplicative weights, theoretical computer science, shortest path, parallel algorithms
Collection: 31st Annual European Symposium on Algorithms (ESA 2023)
Issue Date: 2023
Date of publication: 30.08.2023


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