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Documents authored by Hahn, Niklas


Document
Learning-Augmented Online TSP on Rings, Trees, Flowers and (Almost) Everywhere Else

Authors: Evripidis Bampis, Bruno Escoffier, Themis Gouleakis, Niklas Hahn, Kostas Lakis, Golnoosh Shahkarami, and Michalis Xefteris

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)


Abstract
We study the Online Traveling Salesperson Problem (OLTSP) with predictions. In OLTSP, a sequence of initially unknown requests arrive over time at points (locations) of a metric space. The goal is, starting from a particular point of the metric space (the origin), to serve all these requests while minimizing the total time spent. The server moves with unit speed or is "waiting" (zero speed) at some location. We consider two variants: in the open variant, the goal is achieved when the last request is served. In the closed one, the server additionally has to return to the origin. We adopt a prediction model, introduced for OLTSP on the line [Gouleakis et al., 2023], in which the predictions correspond to the locations of the requests and extend it to more general metric spaces. We first propose an oracle-based algorithmic framework, inspired by previous work [Bampis et al., 2023]. This framework allows us to design online algorithms for general metric spaces that provide competitive ratio guarantees which, given perfect predictions, beat the best possible classical guarantee (consistency). Moreover, they degrade gracefully along with the increase in error (smoothness), but always within a constant factor of the best known competitive ratio in the classical case (robustness). Having reduced the problem to designing suitable efficient oracles, we describe how to achieve this for general metric spaces as well as specific metric spaces (rings, trees and flowers), the resulting algorithms being tractable in the latter case. The consistency guarantees of our algorithms are tight in almost all cases, and their smoothness guarantees only suffer a linear dependency on the error, which we show is necessary. Finally, we provide robustness guarantees improving previous results.

Cite as

Evripidis Bampis, Bruno Escoffier, Themis Gouleakis, Niklas Hahn, Kostas Lakis, Golnoosh Shahkarami, and Michalis Xefteris. Learning-Augmented Online TSP on Rings, Trees, Flowers and (Almost) Everywhere Else. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 12:1-12:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{bampis_et_al:LIPIcs.ESA.2023.12,
  author =	{Bampis, Evripidis and Escoffier, Bruno and Gouleakis, Themis and Hahn, Niklas and Lakis, Kostas and Shahkarami, Golnoosh and Xefteris, Michalis},
  title =	{{Learning-Augmented Online TSP on Rings, Trees, Flowers and (Almost) Everywhere Else}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{12:1--12:17},
  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/entities/document/10.4230/LIPIcs.ESA.2023.12},
  URN =		{urn:nbn:de:0030-drops-186659},
  doi =		{10.4230/LIPIcs.ESA.2023.12},
  annote =	{Keywords: TSP, Online algorithms, Learning-augmented algorithms, Algorithms with predictions, Competitive analysis}
}
Document
The Covering Canadian Traveller Problem Revisited

Authors: Niklas Hahn and Michalis Xefteris

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)


Abstract
In this paper, we consider the k-Covering Canadian Traveller Problem (k-CCTP), which can be seen as a variant of the Travelling Salesperson Problem. The goal of k-CCTP is finding the shortest tour for a traveller to visit a set of locations in a given graph and return to the origin. Crucially, unknown to the traveller, up to k edges of the graph are blocked and the traveller only discovers blocked edges online at one of their respective endpoints. The currently best known upper bound for k-CCTP is O(√k) which was shown in [Huang and Liao, ISAAC '12]. We improve this polynomial bound to a logarithmic one by presenting a deterministic O(log k)-competitive algorithm that runs in polynomial time. Further, we demonstrate the tightness of our analysis by giving a lower bound instance for our algorithm.

Cite as

Niklas Hahn and Michalis Xefteris. The Covering Canadian Traveller Problem Revisited. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 53:1-53:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{hahn_et_al:LIPIcs.MFCS.2023.53,
  author =	{Hahn, Niklas and Xefteris, Michalis},
  title =	{{The Covering Canadian Traveller Problem Revisited}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{53:1--53:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.53},
  URN =		{urn:nbn:de:0030-drops-185876},
  doi =		{10.4230/LIPIcs.MFCS.2023.53},
  annote =	{Keywords: Online Algorithm, Canadian Traveller Problem, Travelling Salesperson Problem, Graph Exploration}
}
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