4 Search Results for "Huang, Wen-Hung"

Document
DOI: 10.4230/LIPIcs.STACS.2023.37
Approximate Selection with Unreliable Comparisons in Optimal Expected Time

Authors: Shengyu Huang, Chih-Hung Liu, and Daniel Rutschmann

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

Abstract
Given n elements, an integer k ≤ n/2 and a parameter ε ≥ 1/n, we study the problem of selecting an element with rank in (k-nε, k+nε] using unreliable comparisons where the outcome of each comparison is incorrect independently with a constant error probability, and multiple comparisons between the same pair of elements are independent. In this fault model, the fundamental problems of finding the minimum, selecting the k-th smallest element and sorting have been shown to require Θ(n log 1/Q), Θ(n log k/Q) and Θ(n log n/Q) comparisons, respectively, to achieve success probability 1-Q [Uriel Feige et al., 1994]. Considering the increasing complexity of modern computing, it is of great interest to develop approximation algorithms that enable a trade-off between the solution quality and the number of comparisons. In particular, approximation algorithms would even be able to attain a sublinear number of comparisons. Very recently, Leucci and Liu [Stefano Leucci and Chih-Hung Liu, 2022] proved that the approximate minimum selection problem, which covers the case that k ≤ nε, requires expected Θ(ε^{-1} log 1/Q) comparisons, but the general case, i.e., for nε < k ≤ n/2, is still open. We develop a randomized algorithm that performs expected O(k/n ε^{-2} log 1/Q) comparisons to achieve success probability at least 1-Q. For k = n ε, the number of comparisons is O(ε^{-1} log 1/Q), matching Leucci and Liu’s result [Stefano Leucci and Chih-Hung Liu, 2022], whereas for k = n/2 (i.e., approximating the median), the number of comparisons is O(ε^{-2} log 1/Q). We also prove that even in the absence of comparison faults, any randomized algorithm with success probability at least 1-Q performs expected Ω(min{n, k/n ε^{-2} log 1/Q}) comparisons. As long as n is large enough, i.e., when n = Ω(k/n ε^{-2} log 1/Q), our lower bound demonstrates the optimality of our algorithm, which covers the possible range of attaining a sublinear number of comparisons. Surprisingly, for constant Q, our algorithm performs expected O(k/n ε^{-2}) comparisons, matching the best possible approximation algorithm in the absence of computation faults. In contrast, for the exact selection problem, the expected number of comparisons is Θ(n log k) with faults versus Θ(n) without faults. Our results also indicate a clear distinction between approximating the minimum and approximating the k-th smallest element, which holds even for the high probability guarantee, e.g., if k = n/2, Q = 1/n and ε = n^{-α} for α ∈ (0, 1/2), the asymptotic difference is almost quadratic, i.e., Θ̃(n^α) versus Θ̃(n^{2α}).
Cite as

Shengyu Huang, Chih-Hung Liu, and Daniel Rutschmann. Approximate Selection with Unreliable Comparisons in Optimal Expected Time. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 37:1-37:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{huang_et_al:LIPIcs.STACS.2023.37,
  author =	{Huang, Shengyu and Liu, Chih-Hung and Rutschmann, Daniel},
  title =	{{Approximate Selection with Unreliable Comparisons in Optimal Expected Time}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{37:1--37:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.37},
  URN =		{urn:nbn:de:0030-drops-176898},
  doi =		{10.4230/LIPIcs.STACS.2023.37},
  annote =	{Keywords: Approximate Selection, Unreliable Comparisons, Independent Faults}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.28
Beyond-Planarity: Turán-Type Results for Non-Planar Bipartite Graphs

Authors: Patrizio Angelini, Michael A. Bekos, Michael Kaufmann, Maximilian Pfister, and Torsten Ueckerdt

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
Beyond-planarity focuses on the study of geometric and topological graphs that are in some sense nearly planar. Here, planarity is relaxed by allowing edge crossings, but only with respect to some local forbidden crossing configurations. Early research dates back to the 1960s (e.g., Avital and Hanani 1966) for extremal problems on geometric graphs, but is also related to graph drawing problems where visual clutter due to edge crossings should be minimized (e.g., Huang et al. 2018). Most of the literature focuses on Turán-type problems, which ask for the maximum number of edges a beyond-planar graph can have. Here, we study this problem for bipartite topological graphs, considering several types of beyond-planar graphs, i.e. 1-planar, 2-planar, fan-planar, and RAC graphs. We prove bounds on the number of edges that are tight up to additive constants; some of them are surprising and not along the lines of the known results for non-bipartite graphs. Our findings lead to an improvement of the leading constant of the well-known Crossing Lemma for bipartite graphs, as well as to a number of interesting questions on topological graphs.
Cite as

Patrizio Angelini, Michael A. Bekos, Michael Kaufmann, Maximilian Pfister, and Torsten Ueckerdt. Beyond-Planarity: Turán-Type Results for Non-Planar Bipartite Graphs. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 28:1-28:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{angelini_et_al:LIPIcs.ISAAC.2018.28,
  author =	{Angelini, Patrizio and Bekos, Michael A. and Kaufmann, Michael and Pfister, Maximilian and Ueckerdt, Torsten},
  title =	{{Beyond-Planarity: Tur\'{a}n-Type Results for Non-Planar Bipartite Graphs}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{28:1--28:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.28},
  URN =		{urn:nbn:de:0030-drops-99763},
  doi =		{10.4230/LIPIcs.ISAAC.2018.28},
  annote =	{Keywords: Bipartite topological graphs, beyond planarity, density, Crossing Lemma}
}
Document
DOI: 10.4230/LITES-v005-i001-a002
Errata for Three Papers (2004-05) on Fixed-Priority Scheduling with Self-Suspensions

Authors: Konstantinos Bletsas, Neil C. Audsley, Wen-Hung Huang, Jian-Jia Chen, and Geoffrey Nelissen

Published in: LITES, Volume 5, Issue 1 (2018). Leibniz Transactions on Embedded Systems, Volume 5, Issue 1

Abstract
The purpose of this article is to (i) highlight the flaws in three previously published works [Audsley, 2004a; Audsley, 2004b; Bletsas, 2005] on the worst-case response time analysis for tasks with self-suspensions and (ii) provide straightforward fixes for those flaws, hence rendering the analysis safe.
Cite as

Konstantinos Bletsas, Neil C. Audsley, Wen-Hung Huang, Jian-Jia Chen, and Geoffrey Nelissen. Errata for Three Papers (2004-05) on Fixed-Priority Scheduling with Self-Suspensions. In LITES, Volume 5, Issue 1 (2018). Leibniz Transactions on Embedded Systems, Volume 5, Issue 1, pp. 02:1-02:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@Article{bletsas_et_al:LITES-v005-i001-a002,
  author =	{Bletsas, Konstantinos and Audsley, Neil C. and Huang, Wen-Hung and Chen, Jian-Jia and Nelissen, Geoffrey},
  title =	{{Errata for Three Papers (2004-05) on Fixed-Priority Scheduling with Self-Suspensions}},
  journal =	{Leibniz Transactions on Embedded Systems},
  pages =	{02:1--02:20},
  ISSN =	{2199-2002},
  year =	{2018},
  volume =	{5},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LITES-v005-i001-a002},
  doi =		{10.4230/LITES-v005-i001-a002},
  annote =	{Keywords: real-time, scheduling, self-suspension, worst-case response time analysis}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2017.9
On the Pitfalls of Resource Augmentation Factors and Utilization Bounds in Real-Time Scheduling

Authors: Jian-Jia Chen, Georg von der Brüggen, Wen-Hung Huang, and Robert I. Davis

Published in: LIPIcs, Volume 76, 29th Euromicro Conference on Real-Time Systems (ECRTS 2017)

Abstract
In this paper, we take a careful look at speedup factors, utilization bounds, and capacity augmentation bounds. These three metrics have been widely adopted in real-time scheduling research as the de facto standard theoretical tools for assessing scheduling algorithms and schedulability tests. Despite that, it is not always clear how researchers and designers should interpret or use these metrics. In studying this area, we found a number of surprising results, and related to them, ways in which the metrics may be misinterpreted or misunderstood. In this paper, we provide a perspective on the use of these metrics, guiding researchers on their meaning and interpretation, and helping to avoid pitfalls in their use. Finally, we propose and demonstrate the use of parametric augmentation functions as a means of providing nuanced information that may be more relevant in practical settings.
Cite as

Jian-Jia Chen, Georg von der Brüggen, Wen-Hung Huang, and Robert I. Davis. On the Pitfalls of Resource Augmentation Factors and Utilization Bounds in Real-Time Scheduling. In 29th Euromicro Conference on Real-Time Systems (ECRTS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 76, pp. 9:1-9:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chen_et_al:LIPIcs.ECRTS.2017.9,
  author =	{Chen, Jian-Jia and von der Br\"{u}ggen, Georg and Huang, Wen-Hung and Davis, Robert I.},
  title =	{{On the Pitfalls of Resource Augmentation Factors and Utilization Bounds in Real-Time Scheduling}},
  booktitle =	{29th Euromicro Conference on Real-Time Systems (ECRTS 2017)},
  pages =	{9:1--9:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-037-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{76},
  editor =	{Bertogna, Marko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2017.9},
  URN =		{urn:nbn:de:0030-drops-71619},
  doi =		{10.4230/LIPIcs.ECRTS.2017.9},
  annote =	{Keywords: Real-time systems, speedup factors, utilization bounds, capacity augmentation bounds}
}
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