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Documents authored by Lakis, Kostas

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RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.74
Improved Bounds for Graph Distances in Scale Free Percolation and Related Models

Authors: Kostas Lakis, Johannes Lengler, Kalina Petrova, and Leon Schiller

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
In this paper, we study graph distances in the geometric random graph models scale-free percolation SFP, geometric inhomogeneous random graphs GIRG, and hyperbolic random graphs HRG. Despite the wide success of the models, the parameter regime in which graph distances are polylogarithmic is poorly understood. We provide new and improved lower bounds. In a certain portion of the parameter regime, those match the known upper bounds. Compared to the best previous lower bounds by Hao and Heydenreich [Hao and Heydenreich, 2023], our result has several advantages: it gives matching bounds for a larger range of parameters, thus settling the question for a larger portion of the parameter space. It strictly improves the lower bounds of [Hao and Heydenreich, 2023] for all parameters settings in which those bounds were not tight. It gives tail bounds on the probability of having short paths, which imply shape theorems for the k-neighbourhood of a vertex whenever our lower bounds are tight, and tight bounds for the size of this k-neighbourhood. And last but not least, our proof is much simpler and not much longer than two pages, and we demonstrate that it generalizes well by showing that the same technique also works for first passage percolation.
Cite as

Kostas Lakis, Johannes Lengler, Kalina Petrova, and Leon Schiller. Improved Bounds for Graph Distances in Scale Free Percolation and Related Models. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 74:1-74:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{lakis_et_al:LIPIcs.APPROX/RANDOM.2024.74,
  author =	{Lakis, Kostas and Lengler, Johannes and Petrova, Kalina and Schiller, Leon},
  title =	{{Improved Bounds for Graph Distances in Scale Free Percolation and Related Models}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{74:1--74:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.74},
  URN =		{urn:nbn:de:0030-drops-210676},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.74},
  annote =	{Keywords: Mathematics, Probability Theory, Combinatorics, Random Graphs, Random Metric Spaces}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.12
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}
}
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