Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Mestre, Julián; Pupyrev, Sergey; Umboh, Seeun William https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-154751
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On the Extended TSP Problem

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Abstract

We initiate the theoretical study of Ext-TSP, a problem that originates in the area of profile-guided binary optimization. Given a graph G = (V, E) with positive edge weights w: E → R^+, and a non-increasing discount function f(⋅) such that f(1) = 1 and f(i) = 0 for i > k, for some parameter k that is part of the problem definition. The problem is to sequence the vertices V so as to maximize ∑_{(u, v) ∈ E} f(|d_u - d_v|)⋅ w(u,v), where d_v ∈ {1, …, |V|} is the position of vertex v in the sequence.
We show that Ext-TSP is APX-hard to approximate in general and we give a (k+1)-approximation algorithm for general graphs and a PTAS for some sparse graph classes such as planar or treewidth-bounded graphs.
Interestingly, the problem remains challenging even on very simple graph classes; indeed, there is no exact n^o(k) time algorithm for trees unless the ETH fails. We complement this negative result with an exact n^O(k) time algorithm for trees.

BibTeX - Entry

@InProceedings{mestre_et_al:LIPIcs.ISAAC.2021.42,
  author =	{Mestre, Juli\'{a}n and Pupyrev, Sergey and Umboh, Seeun William},
  title =	{{On the Extended TSP Problem}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{42:1--42:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/15475},
  URN =		{urn:nbn:de:0030-drops-154751},
  doi =		{10.4230/LIPIcs.ISAAC.2021.42},
  annote =	{Keywords: profile-guided optimization, approximation algorithms, bandwidth, TSP}
}

Keywords: profile-guided optimization, approximation algorithms, bandwidth, TSP
Seminar: 32nd International Symposium on Algorithms and Computation (ISAAC 2021)
Issue date: 2021
Date of publication: 30.11.2021


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