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Documents authored by Zhao, Yiming

Document
DOI: 10.4230/LIPIcs.STACS.2025.76
Dynamic Unit-Disk Range Reporting

Authors: Haitao Wang and Yiming Zhao

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
For a set P of n points in the plane and a value r > 0, the unit-disk range reporting problem is to construct a data structure so that given any query disk of radius r, all points of P in the disk can be reported efficiently. We consider the dynamic version of the problem where point insertions and deletions of P are allowed. The previous best method provides a data structure of O(n log n) space that supports O(log^{3+ε} n) amortized insertion time, O(log^{5+ε} n) amortized deletion time, and O(log² n/log log n+k) query time, where ε is an arbitrarily small positive constant and k is the output size. In this paper, we improve the query time to O(log n+k) while keeping other complexities the same as before. A key ingredient of our approach is a shallow cutting algorithm for circular arcs, which may be interesting in its own right. A related problem that can also be solved by our techniques is the dynamic unit-disk range emptiness queries: Given a query unit disk, we wish to determine whether the disk contains a point of P. The best previous work can maintain P in a data structure of O(n) space that supports O(log² n) amortized insertion time, O(log⁴n) amortized deletion time, and O(log² n) query time. Our new data structure also uses O(n) space but can support each update in O(log^{1+ε} n) amortized time and support each query in O(log n) time.
Cite as

Haitao Wang and Yiming Zhao. Dynamic Unit-Disk Range Reporting. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 76:1-76:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{wang_et_al:LIPIcs.STACS.2025.76,
  author =	{Wang, Haitao and Zhao, Yiming},
  title =	{{Dynamic Unit-Disk Range Reporting}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{76:1--76:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.76},
  URN =		{urn:nbn:de:0030-drops-229019},
  doi =		{10.4230/LIPIcs.STACS.2025.76},
  annote =	{Keywords: Unit disks, range reporting, range emptiness, alpha-hulls, dynamic data structures, shallow cuttings}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.101
Improved Algorithms for Distance Selection and Related Problems

Authors: Haitao Wang and Yiming Zhao

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

Abstract
In this paper, we propose new techniques for solving geometric optimization problems involving interpoint distances of a point set in the plane. Given a set P of n points in the plane and an integer 1 ≤ k ≤ binom(n,2), the distance selection problem is to find the k-th smallest interpoint distance among all pairs of points of P. The previously best deterministic algorithm solves the problem in O(n^{4/3} log² n) time [Katz and Sharir, 1997]. In this paper, we improve their algorithm to O(n^{4/3} log n) time. Using similar techniques, we also give improved algorithms on both the two-sided and the one-sided discrete Fréchet distance with shortcuts problem for two point sets in the plane. For the two-sided problem (resp., one-sided problem), we improve the previous work [Avraham, Filtser, Kaplan, Katz, and Sharir, 2015] by a factor of roughly log²(m+n) (resp., (m+n)^ε), where m and n are the sizes of the two input point sets, respectively. Other problems whose solutions can be improved by our techniques include the reverse shortest path problems for unit-disk graphs. Our techniques are quite general and we believe they will find many other applications in future.
Cite as

Haitao Wang and Yiming Zhao. Improved Algorithms for Distance Selection and Related Problems. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 101:1-101:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{wang_et_al:LIPIcs.ESA.2023.101,
  author =	{Wang, Haitao and Zhao, Yiming},
  title =	{{Improved Algorithms for Distance Selection and Related Problems}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{101:1--101:14},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.101},
  URN =		{urn:nbn:de:0030-drops-187544},
  doi =		{10.4230/LIPIcs.ESA.2023.101},
  annote =	{Keywords: Geometric optimization, distance selection, Fr\'{e}chet distance, range searching}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.82
Computing the Minimum Bottleneck Moving Spanning Tree

Authors: Haitao Wang and Yiming Zhao

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
Given a set P of n points that are moving in the plane, we consider the problem of computing a spanning tree for these moving points that does not change its combinatorial structure during the point movement. The objective is to minimize the bottleneck weight of the spanning tree (i.e., the largest Euclidean length of all edges) during the whole movement. The problem was solved in O(n²) time previously [Akitaya, Biniaz, Bose, De Carufel, Maheshwari, Silveira, and Smid, WADS 2021]. In this paper, we present a new algorithm of O(n^{4/3} log³ n) time.
Cite as

Haitao Wang and Yiming Zhao. Computing the Minimum Bottleneck Moving Spanning Tree. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 82:1-82:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{wang_et_al:LIPIcs.MFCS.2022.82,
  author =	{Wang, Haitao and Zhao, Yiming},
  title =	{{Computing the Minimum Bottleneck Moving Spanning Tree}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{82:1--82:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.82},
  URN =		{urn:nbn:de:0030-drops-168801},
  doi =		{10.4230/LIPIcs.MFCS.2022.82},
  annote =	{Keywords: minimum spanning tree, moving points, unit-disk range emptiness query, dynamic data structure}
}
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