5 Search Results for "Lindermayr, Alexander"

Document
DOI: 10.4230/LIPIcs.ESA.2024.47
Bicriterial Approximation for the Incremental Prize-Collecting Steiner-Tree Problem

Authors: Yann Disser, Svenja M. Griesbach, Max Klimm, and Annette Lutz

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
We consider an incremental variant of the rooted prize-collecting Steiner-tree problem with a growing budget constraint. While no incremental solution exists that simultaneously approximates the optimum for all budgets, we show that a bicriterial (α,μ)-approximation is possible, i.e., a solution that with budget B+α for all B ∈ ℝ_{≥ 0} is a multiplicative μ-approximation compared to the optimum solution with budget B. For the case that the underlying graph is a tree, we present a polynomial-time density-greedy algorithm that computes a (χ,1)-approximation, where χ denotes the eccentricity of the root vertex in the underlying graph, and show that this is best possible. An adaptation of the density-greedy algorithm for general graphs is (γ,2)-competitive where γ is the maximal length of a vertex-disjoint path starting in the root. While this algorithm does not run in polynomial time, it can be adapted to a (γ,3)-competitive algorithm that runs in polynomial time. We further devise a capacity-scaling algorithm that guarantees a (3χ,8)-approximation and, more generally, a ((4𝓁 - 1)χ, (2^{𝓁 + 2})/(2^𝓁 -1))-approximation for every fixed 𝓁 ∈ ℕ.
Cite as

Yann Disser, Svenja M. Griesbach, Max Klimm, and Annette Lutz. Bicriterial Approximation for the Incremental Prize-Collecting Steiner-Tree Problem. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 47:1-47:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{disser_et_al:LIPIcs.ESA.2024.47,
  author =	{Disser, Yann and Griesbach, Svenja M. and Klimm, Max and Lutz, Annette},
  title =	{{Bicriterial Approximation for the Incremental Prize-Collecting Steiner-Tree Problem}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{47:1--47:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.47},
  URN =		{urn:nbn:de:0030-drops-211188},
  doi =		{10.4230/LIPIcs.ESA.2024.47},
  annote =	{Keywords: incremental optimization, competitive analysis, prize-collecting Steiner-tree}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.72
Connectivity Oracles for Predictable Vertex Failures

Authors: Bingbing Hu, Evangelos Kosinas, and Adam Polak

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
The problem of designing connectivity oracles supporting vertex failures is one of the basic data structures problems for undirected graphs. It is already well understood: previous works [Duan-Pettie STOC'10; Long-Saranurak FOCS'22] achieve query time linear in the number of failed vertices, and it is conditionally optimal as long as we require preprocessing time polynomial in the size of the graph and update time polynomial in the number of failed vertices. We revisit this problem in the paradigm of algorithms with predictions: we ask if the query time can be improved if the set of failed vertices can be predicted beforehand up to a small number of errors. More specifically, we design a data structure that, given a graph G = (V,E) and a set of vertices predicted to fail D̂ ⊆ V of size d = |D̂|, preprocesses it in time Õ(d|E|) and then can receive an update given as the symmetric difference between the predicted and the actual set of failed vertices D̂△D = (D̂ ⧵ D) ∪ (D ⧵ D̂) of size η = |D̂△D|, process it in time Õ(η⁴), and after that answer connectivity queries in G ⧵ D in time O(η). Viewed from another perspective, our data structure provides an improvement over the state of the art for the fully dynamic subgraph connectivity problem in the sensitivity setting [Henzinger-Neumann ESA'16]. We argue that the preprocessing time and query time of our data structure are conditionally optimal under standard fine-grained complexity assumptions.
Cite as

Bingbing Hu, Evangelos Kosinas, and Adam Polak. Connectivity Oracles for Predictable Vertex Failures. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 72:1-72:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hu_et_al:LIPIcs.ESA.2024.72,
  author =	{Hu, Bingbing and Kosinas, Evangelos and Polak, Adam},
  title =	{{Connectivity Oracles for Predictable Vertex Failures}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{72:1--72:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.72},
  URN =		{urn:nbn:de:0030-drops-211437},
  doi =		{10.4230/LIPIcs.ESA.2024.72},
  annote =	{Keywords: Data structures, graph connectivity, algorithms with predictions}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.2
Online Time-Windows TSP with Predictions

Authors: Shuchi Chawla and Dimitris Christou

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

Abstract
In the Time-Windows TSP (TW-TSP) we are given requests at different locations on a network; each request is endowed with a reward and an interval of time; the goal is to find a tour that visits as much reward as possible during the corresponding time window. For the online version of this problem, where each request is revealed at the start of its time window, no finite competitive ratio can be obtained. We consider a version of the problem where the algorithm is presented with predictions of where and when the online requests will appear, without any knowledge of the quality of this side information. Vehicle routing problems such as the TW-TSP can be very sensitive to errors or changes in the input due to the hard time-window constraints, and it is unclear whether imperfect predictions can be used to obtain a finite competitive ratio. We show that good performance can be achieved by explicitly building slack into the solution. Our main result is an online algorithm that achieves a competitive ratio logarithmic in the diameter of the underlying network, matching the performance of the best offline algorithm to within factors that depend on the quality of the provided predictions. The competitive ratio degrades smoothly as a function of the quality and we show that this dependence is tight within constant factors.
Cite as

Shuchi Chawla and Dimitris Christou. Online Time-Windows TSP with Predictions. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 2:1-2:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chawla_et_al:LIPIcs.APPROX/RANDOM.2024.2,
  author =	{Chawla, Shuchi and Christou, Dimitris},
  title =	{{Online Time-Windows TSP with Predictions}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{2:1--2:21},
  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.2024.2},
  URN =		{urn:nbn:de:0030-drops-209954},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.2},
  annote =	{Keywords: Travelling Salesman Problem, Predictions, Learning-Augmented Algorithms, Approximation}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.99
Double Coverage with Machine-Learned Advice

Authors: Alexander Lindermayr, Nicole Megow, and Bertrand Simon

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
We study the fundamental online k-server problem in a learning-augmented setting. While in the traditional online model, an algorithm has no information about the request sequence, we assume that there is given some advice (e.g. machine-learned predictions) on an algorithm’s decision. There is, however, no guarantee on the quality of the prediction and it might be far from being correct. Our main result is a learning-augmented variation of the well-known Double Coverage algorithm for k-server on the line (Chrobak et al., SIDMA 1991) in which we integrate predictions as well as our trust into their quality. We give an error-dependent competitive ratio, which is a function of a user-defined confidence parameter, and which interpolates smoothly between an optimal consistency, the performance in case that all predictions are correct, and the best-possible robustness regardless of the prediction quality. When given good predictions, we improve upon known lower bounds for online algorithms without advice. We further show that our algorithm achieves for any k an almost optimal consistency-robustness tradeoff, within a class of deterministic algorithms respecting local and memoryless properties. Our algorithm outperforms a previously proposed (more general) learning-augmented algorithm. It is remarkable that the previous algorithm crucially exploits memory, whereas our algorithm is memoryless. Finally, we demonstrate in experiments the practicability and the superior performance of our algorithm on real-world data.
Cite as

Alexander Lindermayr, Nicole Megow, and Bertrand Simon. Double Coverage with Machine-Learned Advice. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 99:1-99:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lindermayr_et_al:LIPIcs.ITCS.2022.99,
  author =	{Lindermayr, Alexander and Megow, Nicole and Simon, Bertrand},
  title =	{{Double Coverage with Machine-Learned Advice}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{99:1--99:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.99},
  URN =		{urn:nbn:de:0030-drops-156954},
  doi =		{10.4230/LIPIcs.ITCS.2022.99},
  annote =	{Keywords: online k-server problem, competitive analysis, learning-augmented algorithms, untrusted predictions, consistency, robustness}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.65
Elimination Distance to Bounded Degree on Planar Graphs

Authors: Alexander Lindermayr, Sebastian Siebertz, and Alexandre Vigny

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
We study the graph parameter elimination distance to bounded degree, which was introduced by Bulian and Dawar in their study of the parameterized complexity of the graph isomorphism problem. We prove that the problem is fixed-parameter tractable on planar graphs, that is, there exists an algorithm that given a planar graph G and integers d and k decides in time f(k,d)⋅ n^c for a computable function f and constant c whether the elimination distance of G to the class of degree d graphs is at most k.
Cite as

Alexander Lindermayr, Sebastian Siebertz, and Alexandre Vigny. Elimination Distance to Bounded Degree on Planar Graphs. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 65:1-65:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{lindermayr_et_al:LIPIcs.MFCS.2020.65,
  author =	{Lindermayr, Alexander and Siebertz, Sebastian and Vigny, Alexandre},
  title =	{{Elimination Distance to Bounded Degree on Planar Graphs}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{65:1--65:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.65},
  URN =		{urn:nbn:de:0030-drops-127557},
  doi =		{10.4230/LIPIcs.MFCS.2020.65},
  annote =	{Keywords: Elimination distance, parameterized complexity, structural graph theory}
}
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