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Documents authored by Wei, Zhewei


Document
Track A: Algorithms, Complexity and Games
On Range Summary Queries

Authors: Peyman Afshani, Pingan Cheng, Aniket Basu Roy, and Zhewei Wei

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)


Abstract
We study the query version of the approximate heavy hitter and quantile problems. In the former problem, the input is a parameter ε and a set P of n points in ℝ^d where each point is assigned a color from a set C, and the goal is to build a structure such that given any geometric range γ, we can efficiently find a list of approximate heavy hitters in γ∩P, i.e., colors that appear at least ε |γ∩P| times in γ∩P, as well as their frequencies with an additive error of ε |γ∩P|. In the latter problem, each point is assigned a weight from a totally ordered universe and the query must output a sequence S of 1+1/ε weights such that the i-th weight in S has approximate rank iε|γ∩P|, meaning, rank iε|γ∩P| up to an additive error of ε|γ∩P|. Previously, optimal results were only known in 1D [Wei and Yi, 2011] but a few sub-optimal methods were available in higher dimensions [Peyman Afshani and Zhewei Wei, 2017; Pankaj K. Agarwal et al., 2012]. We study the problems for two important classes of geometric ranges: 3D halfspace and 3D dominance queries. It is known that many other important queries can be reduced to these two, e.g., 1D interval stabbing or interval containment, 2D three-sided queries, 2D circular as well as 2D k-nearest neighbors queries. We consider the real RAM model of computation where integer registers of size w bits, w = Θ(log n), are also available. For dominance queries, we show optimal solutions for both heavy hitter and quantile problems: using linear space, we can answer both queries in time O(log n + 1/ε). Note that as the output size is 1/ε, after investing the initial O(log n) searching time, our structure takes on average O(1) time to find a heavy hitter or a quantile! For more general halfspace heavy hitter queries, the same optimal query time can be achieved by increasing the space by an extra log_w(1/ε) (resp. log log_w(1/ε)) factor in 3D (resp. 2D). By spending extra log^O(1)(1/ε) factors in both time and space, we can also support quantile queries. We remark that it is hopeless to achieve a similar query bound for dimensions 4 or higher unless significant advances are made in the data structure side of theory of geometric approximations.

Cite as

Peyman Afshani, Pingan Cheng, Aniket Basu Roy, and Zhewei Wei. On Range Summary Queries. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 7:1-7:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{afshani_et_al:LIPIcs.ICALP.2023.7,
  author =	{Afshani, Peyman and Cheng, Pingan and Basu Roy, Aniket and Wei, Zhewei},
  title =	{{On Range Summary Queries}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{7:1--7:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.7},
  URN =		{urn:nbn:de:0030-drops-180590},
  doi =		{10.4230/LIPIcs.ICALP.2023.7},
  annote =	{Keywords: Computational Geometry, Range Searching, Random Sampling, Geometric Approximation, Data Structures and Algorithms}
}
Document
Complete Volume
LIPIcs, Volume 186, ICDT 2021, Complete Volume

Authors: Ke Yi and Zhewei Wei

Published in: LIPIcs, Volume 186, 24th International Conference on Database Theory (ICDT 2021)


Abstract
LIPIcs, Volume 186, ICDT 2021, Complete Volume

Cite as

Ke Yi and Zhewei Wei. LIPIcs, Volume 186, ICDT 2021, Complete Volume. In 24th International Conference on Database Theory (ICDT 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 186, pp. 1-438, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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@Proceedings{yi_et_al:LIPIcs.ICDT.2021,
  title =	{{LIPIcs, Volume 186, ICDT 2021, Complete Volume}},
  booktitle =	{24th International Conference on Database Theory (ICDT 2021)},
  pages =	{1--438},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-179-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{186},
  editor =	{Yi, Ke and Wei, Zhewei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2021},
  URN =		{urn:nbn:de:0030-drops-137076},
  doi =		{10.4230/LIPIcs.ICDT.2021},
  annote =	{Keywords: LIPIcs, Volume 186, ICDT 2021, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Ke Yi and Zhewei Wei

Published in: LIPIcs, Volume 186, 24th International Conference on Database Theory (ICDT 2021)


Abstract
Front Matter, Table of Contents, Preface, Conference Organization

Cite as

Ke Yi and Zhewei Wei. Front Matter, Table of Contents, Preface, Conference Organization. In 24th International Conference on Database Theory (ICDT 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 186, pp. 0:i-0:xvi, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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@InProceedings{yi_et_al:LIPIcs.ICDT.2021.0,
  author =	{Yi, Ke and Wei, Zhewei},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{24th International Conference on Database Theory (ICDT 2021)},
  pages =	{0:i--0:xvi},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-179-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{186},
  editor =	{Yi, Ke and Wei, Zhewei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2021.0},
  URN =		{urn:nbn:de:0030-drops-137086},
  doi =		{10.4230/LIPIcs.ICDT.2021.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Independent Range Sampling, Revisited

Authors: Peyman Afshani and Zhewei Wei

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)


Abstract
In the independent range sampling (IRS) problem, given an input set P of n points in R^d, the task is to build a data structure, such that given a range R and an integer t >= 1, it returns t points that are uniformly and independently drawn from P cap R. The samples must satisfy inter-query independence, that is, the samples returned by every query must be independent of the samples returned by all the previous queries. This problem was first tackled by Hu, Qiao and Tao in 2014, who proposed optimal structures for one-dimensional dynamic IRS problem in internal memory and one-dimensional static IRS problem in external memory. In this paper, we study two natural extensions of the independent range sampling problem. In the first extension, we consider the static IRS problem in two and three dimensions in internal memory. We obtain data structures with optimal space-query tradeoffs for 3D halfspace, 3D dominance, and 2D three-sided queries. The second extension considers weighted IRS problem. Each point is associated with a real-valued weight, and given a query range R, a sample is drawn independently such that each point in P cap R is selected with probability proportional to its weight. Walker's alias method is a classic solution to this problem when no query range is specified. We obtain optimal data structure for one dimensional weighted range sampling problem, thereby extending the alias method to allow range queries.

Cite as

Peyman Afshani and Zhewei Wei. Independent Range Sampling, Revisited. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 3:1-3:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)


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@InProceedings{afshani_et_al:LIPIcs.ESA.2017.3,
  author =	{Afshani, Peyman and Wei, Zhewei},
  title =	{{Independent Range Sampling, Revisited}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{3:1--3:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.3},
  URN =		{urn:nbn:de:0030-drops-78592},
  doi =		{10.4230/LIPIcs.ESA.2017.3},
  annote =	{Keywords: data structures, range searching, range sampling, random sampling}
}
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