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Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2020.52
URN: urn:nbn:de:0030-drops-129183
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12918/
Friggstad, Zachary ;
Swamy, Chaitanya
A Constant-Factor Approximation for Directed Latency in Quasi-Polynomial Time
Abstract
We consider the directed minimum latency problem (DirLat), wherein we seek a path P visiting all points (or clients) in a given asymmetric metric starting at a given root node r, so as to minimize the sum of the client waiting times, where the waiting time of a client v is the length of the r-v portion of P. We give the first constant-factor approximation guarantee for DirLat, but in quasi-polynomial time. Previously, a polynomial-time O(log n)-approximation was known [Z. Friggstad et al., 2013], and no better approximation guarantees were known even in quasi-polynomial time.
A key ingredient of our result, and our chief technical contribution, is an extension of a recent result of [A. Köhne et al., 2019] showing that the integrality gap of the natural Held-Karp relaxation for asymmetric TSP-Path (ATSPP) is at most a constant, which itself builds on the breakthrough similar result established for asymmetric TSP (ATSP) by Svensson et al. [O. Svensson et al., 2018]. We show that the integrality gap of the Held-Karp relaxation for ATSPP is bounded by a constant even if the cut requirements of the LP relaxation are relaxed from x(δ^{in}(S)) ≥ 1 to x(δ^{in}(S)) ≥ ρ for some constant 1/2 < ρ ≤ 1.
We also give a better approximation guarantee for the minimum total-regret problem, where the goal is to find a path P that minimizes the total time that nodes spend in excess of their shortest-path distances from r, which can be cast as a special case of DirLat involving so-called regret metrics.
BibTeX - Entry
@InProceedings{friggstad_et_al:LIPIcs:2020:12918,
author = {Zachary Friggstad and Chaitanya Swamy},
title = {{A Constant-Factor Approximation for Directed Latency in Quasi-Polynomial Time}},
booktitle = {28th Annual European Symposium on Algorithms (ESA 2020)},
pages = {52:1--52:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-162-7},
ISSN = {1868-8969},
year = {2020},
volume = {173},
editor = {Fabrizio Grandoni and Grzegorz Herman and Peter Sanders},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12918},
URN = {urn:nbn:de:0030-drops-129183},
doi = {10.4230/LIPIcs.ESA.2020.52},
annote = {Keywords: Approximation Algorithms, Directed Latency, TSP}
}
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Keywords: |
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Approximation Algorithms, Directed Latency, TSP |
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Collection: |
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28th Annual European Symposium on Algorithms (ESA 2020) |
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Issue Date: |
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2020 |
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Date of publication: |
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26.08.2020 |
