4 Search Results for "Lu, Yang"

Document
DOI: 10.4230/LIPIcs.ESA.2023.97
Improved Algorithms for Online Rent Minimization Problem Under Unit-Size Jobs

Authors: Enze Sun, Zonghan Yang, and Yuhao Zhang

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

Abstract
We consider the Online Rent Minimization problem, where online jobs with release times, deadlines, and processing times must be scheduled on machines that can be rented for a fixed length period of T. The objective is to minimize the number of machine rents. This problem generalizes the Online Machine Minimization problem where machines can be rented for an infinite period, and both problems have an asymptotically optimal competitive ratio of O(log(p_max/p_min)) for general processing times, where p_max and p_min are the maximum and minimum processing times respectively. However, for small values of p_max/p_min, a better competitive ratio can be achieved by assuming unit-size jobs. Under this assumption, Devanur et al. (2014) gave an optimal e-competitive algorithm for Online Machine Minimization, and Chen and Zhang (2022) gave a (3e+7) ≈ 15.16-competitive algorithm for Online Rent Minimization. In this paper, we significantly improve the competitive ratio of the Online Rent Minimization problem under unit size to 6, by using a clean oracle-based online algorithm framework.
Cite as

Enze Sun, Zonghan Yang, and Yuhao Zhang. Improved Algorithms for Online Rent Minimization Problem Under Unit-Size Jobs. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 97:1-97:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{sun_et_al:LIPIcs.ESA.2023.97,
  author =	{Sun, Enze and Yang, Zonghan and Zhang, Yuhao},
  title =	{{Improved Algorithms for Online Rent Minimization Problem Under Unit-Size Jobs}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{97:1--97:14},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.97},
  URN =		{urn:nbn:de:0030-drops-187500},
  doi =		{10.4230/LIPIcs.ESA.2023.97},
  annote =	{Keywords: Online Algorithm, Scheduling, Machine Minimization, Rent Minimization}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2017.21
Smart Contract Execution - the (+-)-Biased Ballot Problem

Authors: Lin Chen, Lei Xu, Zhimin Gao, Nolan Shah, Yang Lu, and Weidong Shi

Published in: LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017)

Abstract
Transaction system build on top of blockchain, especially smart contract, is becoming an important part of world economy. However, there is a lack of formal study on the behavior of users in these systems, which leaves the correctness and security of such system without a solid foundation. Unlike mining, in which the reward for mining a block is fixed, different execution results of a smart contract may lead to significantly different payoffs of users, which gives more incentives for some user to follow a branch that contains a wrong result, even if the branch is shorter. It is thus important to understand the exact probability that a branch is being selected by the system. We formulate this problem as the (+-)-Biased Ballot Problem as follows: there are n voters one by one voting for either of the two candidates A and B. The probability of a user voting for A or B depends on whether the difference between the current votes of A and B is positive or negative. Our model takes into account the behavior of three different kinds of users when a branch occurs in the system -- users having preference over a certain branch based on the history of their transactions, and users being indifferent and simply follow the longest chain. We study two important probabilities that are closely related with a blockchain based system - the probability that A wins at last, and the probability that A receives d votes first. We show how to recursively calculate the two probabilities for any fixed n and d, and also discuss their asymptotic values when n and d are sufficiently large.
Cite as

Lin Chen, Lei Xu, Zhimin Gao, Nolan Shah, Yang Lu, and Weidong Shi. Smart Contract Execution - the (+-)-Biased Ballot Problem. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 21:1-21:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chen_et_al:LIPIcs.ISAAC.2017.21,
  author =	{Chen, Lin and Xu, Lei and Gao, Zhimin and Shah, Nolan and Lu, Yang and Shi, Weidong},
  title =	{{Smart Contract Execution - the (+-)-Biased Ballot Problem}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{21:1--21:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Okamoto, Yoshio and Tokuyama, Takeshi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.21},
  URN =		{urn:nbn:de:0030-drops-82388},
  doi =		{10.4230/LIPIcs.ISAAC.2017.21},
  annote =	{Keywords: Blockchain, Probability, Random Walk, Smart Contract}
}
Document
DOI: 10.4230/LIPIcs.STACS.2016.51
FPTAS for Hardcore and Ising Models on Hypergraphs

Authors: Pinyan Lu, Kuan Yang, and Chihao Zhang

Published in: LIPIcs, Volume 47, 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)

Abstract
Hardcore and Ising models are two most important families of two state spin systems in statistic physics. Partition function of spin systems is the center concept in statistic physics which connects microscopic particles and their interactions with their macroscopic and statistical properties of materials such as energy, entropy, ferromagnetism, etc. If each local interaction of the system involves only two particles, the system can be described by a graph. In this case, fully polynomial-time approximation scheme (FPTAS) for computing the partition function of both hardcore and anti-ferromagnetic Ising model was designed up to the uniqueness condition of the system. These result are the best possible since approximately computing the partition function beyond this threshold is NP-hard. In this paper, we generalize these results to general physics systems, where each local interaction may involves multiple particles. Such systems are described by hypergraphs. For hardcore model, we also provide FPTAS up to the uniqueness condition, and for anti-ferromagnetic Ising model, we obtain FPTAS under a slightly stronger condition.
Cite as

Pinyan Lu, Kuan Yang, and Chihao Zhang. FPTAS for Hardcore and Ising Models on Hypergraphs. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 51:1-51:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{lu_et_al:LIPIcs.STACS.2016.51,
  author =	{Lu, Pinyan and Yang, Kuan and Zhang, Chihao},
  title =	{{FPTAS for Hardcore and Ising Models on Hypergraphs}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{51:1--51:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Ollinger, Nicolas and Vollmer, Heribert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2016.51},
  URN =		{urn:nbn:de:0030-drops-57526},
  doi =		{10.4230/LIPIcs.STACS.2016.51},
  annote =	{Keywords: hard-core model, ising model, hypergraph, spatial mixing, correlation decay}
}
Document
DOI: 10.4230/DagSemProc.07281.5
Directed Feedback Vertex Set Problem is FPT

Authors: Jianer Chen, Yang Liu, and Songiian Lu

Published in: Dagstuhl Seminar Proceedings, Volume 7281, Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs (2007)

Abstract
To decide if the {sc parameterized feedback vertex set} problem in directed graph is fixed-parameter tractable is a long standing open problem. In this paper, we prove that the {sc parameterized feedback vertex set} in directed graph is fixed-parameter tractable and give the first FPT algorithm of running time $O((1.48k)^kn^{O(1)})$ for it. As the {sc feedback arc set} problem in directed graph can be transformed to a {sc feedback vertex set} problem in directed graph, hence we also show that the {sc parameterized feedback arc set} problem can be solved in time of $O((1.48k)^kn^{O(1)})$.
Cite as

Jianer Chen, Yang Liu, and Songiian Lu. Directed Feedback Vertex Set Problem is FPT. In Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs. Dagstuhl Seminar Proceedings, Volume 7281, pp. 1-17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{chen_et_al:DagSemProc.07281.5,
  author =	{Chen, Jianer and Liu, Yang and Lu, Songiian},
  title =	{{Directed Feedback Vertex Set Problem is FPT}},
  booktitle =	{Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs},
  pages =	{1--17},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7281},
  editor =	{Erik Demaine and Gregory Z. Gutin and Daniel Marx and Ulrike Stege},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.07281.5},
  URN =		{urn:nbn:de:0030-drops-12333},
  doi =		{10.4230/DagSemProc.07281.5},
  annote =	{Keywords: Directed feedback vertex set problem, parameterized algorithm,}
}
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