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Documents authored by Liu, Hsiang-Hsuan

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.28
Traveling Repairperson, Unrelated Machines, and Other Stories About Average Completion Times

Authors: Marcin Bienkowski, Artur Kraska, and Hsiang-Hsuan Liu

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
We present a unified framework for minimizing average completion time for many seemingly disparate online scheduling problems, such as the traveling repairperson problems (TRP), dial-a-ride problems (DARP), and scheduling on unrelated machines. We construct a simple algorithm that handles all these scheduling problems, by computing and later executing auxiliary schedules, each optimizing a certain function on already seen prefix of the input. The optimized function resembles a prize-collecting variant of the original scheduling problem. By a careful analysis of the interplay between these auxiliary schedules, and later employing the resulting inequalities in a factor-revealing linear program, we obtain improved bounds on the competitive ratio for all these scheduling problems. In particular, our techniques yield a 4-competitive deterministic algorithm for all previously studied variants of online TRP and DARP, and a 3-competitive one for the scheduling on unrelated machines (also with precedence constraints). This improves over currently best ratios for these problems that are 5.14 and 4, respectively. We also show how to use randomization to further reduce the competitive ratios to 1+2/ln 3 < 2.821 and 1+1/ln 2 < 2.443, respectively. The randomized bounds also substantially improve the current state of the art. Our upper bound for DARP contradicts the lower bound of 3 given by Fink et al. (Inf. Process. Lett. 2009); we pinpoint a flaw in their proof.
Cite as

Marcin Bienkowski, Artur Kraska, and Hsiang-Hsuan Liu. Traveling Repairperson, Unrelated Machines, and Other Stories About Average Completion Times. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bienkowski_et_al:LIPIcs.ICALP.2021.28,
  author =	{Bienkowski, Marcin and Kraska, Artur and Liu, Hsiang-Hsuan},
  title =	{{Traveling Repairperson, Unrelated Machines, and Other Stories About Average Completion Times}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{28:1--28:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.28},
  URN =		{urn:nbn:de:0030-drops-140977},
  doi =		{10.4230/LIPIcs.ICALP.2021.28},
  annote =	{Keywords: traveling repairperson problem, dial-a-ride, machine scheduling, unrelated machines, minimizing completion time, competitive analysis, factor-revealing LP}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2019.6
An Improved Online Algorithm for the Traveling Repairperson Problem on a Line

Authors: Marcin Bienkowski and Hsiang-Hsuan Liu

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract
In the online variant of the traveling repairperson problem (TRP), requests arrive in time at points of a metric space X and must be eventually visited by a server. The server starts at a designated point of X and travels at most at unit speed. Each request has a given weight and once the server visits its position, the request is considered serviced; we call such time completion time of the request. The goal is to minimize the weighted sum of completion times of all requests. In this paper, we give a 5.429-competitive deterministic algorithm for line metrics improving over 5.829-competitive solution by Krumke et al. (TCS 2003). Our result is obtained by modifying the schedule by serving requests that are close to the origin first. To compute the competitive ratio of our approach, we use a charging scheme, and later evaluate its properties using a factor-revealing linear program which upper-bounds the competitive ratio.
Cite as

Marcin Bienkowski and Hsiang-Hsuan Liu. An Improved Online Algorithm for the Traveling Repairperson Problem on a Line. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 6:1-6:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bienkowski_et_al:LIPIcs.MFCS.2019.6,
  author =	{Bienkowski, Marcin and Liu, Hsiang-Hsuan},
  title =	{{An Improved Online Algorithm for the Traveling Repairperson Problem on a Line}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{6:1--6:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.6},
  URN =		{urn:nbn:de:0030-drops-109503},
  doi =		{10.4230/LIPIcs.MFCS.2019.6},
  annote =	{Keywords: traveling repairperson problem, competitive analysis, minimizing completion time, factor-revealing LP}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2016.53
Optimal Nonpreemptive Scheduling in a Smart Grid Model

Authors: Fu-Hong Liu, Hsiang-Hsuan Liu, and Prudence W. H. Wong

Published in: LIPIcs, Volume 64, 27th International Symposium on Algorithms and Computation (ISAAC 2016)

Abstract
We study a scheduling problem arising in demand response management in smart grid. Consumers send in power requests with a flexible feasible time interval during which their requests can be served. The grid controller, upon receiving power requests, schedules each request within the specified interval. The electricity cost is measured by a convex function of the load in each timeslot. The objective is to schedule all requests with the minimum total electricity cost. Previous work has studied cases where jobs have unit power requirement and unit duration. We extend the study to arbitrary power requirement and duration, which has been shown to be NP-hard. We give the first online algorithm for the general problem, and prove that the worst case competitive ratio is asymptotically optimal. We also prove that the problem is fixed parameter tractable. Due to space limit, the missing proofs are presented in the full paper.
Cite as

Fu-Hong Liu, Hsiang-Hsuan Liu, and Prudence W. H. Wong. Optimal Nonpreemptive Scheduling in a Smart Grid Model. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 53:1-53:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{liu_et_al:LIPIcs.ISAAC.2016.53,
  author =	{Liu, Fu-Hong and Liu, Hsiang-Hsuan and Wong, Prudence W. H.},
  title =	{{Optimal Nonpreemptive Scheduling in a Smart Grid Model}},
  booktitle =	{27th International Symposium on Algorithms and Computation (ISAAC 2016)},
  pages =	{53:1--53:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-026-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{64},
  editor =	{Hong, Seok-Hee},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2016.53},
  URN =		{urn:nbn:de:0030-drops-68252},
  doi =		{10.4230/LIPIcs.ISAAC.2016.53},
  annote =	{Keywords: Scheduling, Smart Grid, Convex function cost, Fixed parameter tractable, Online algorithms, Non-preemptive}
}
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