7 Search Results for "Li, Guangping"

Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.1
Approximation Schemes for Orienteering and Deadline TSP in Doubling Metrics

Authors: Kinter Ren and Mohammad R. Salavatipour

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
In this paper we look at various extensions of the classic Traveling Salesman Problem (TSP) on graphs with bounded doubling dimension and bounded treewidth and present approximation schemes for them. Suppose we are given a weighted graph G = (V,E) with a start node s ∈ V, distances on the edges d:E → ℚ^+ and integer k. In k-stroll problem the goal is to find a path from s of minimum length that visits at least k vertices. In k-path we are given an additional end node t ∈ V and the path is supposed to go from s to t. The dual problem to k-stroll is the rooted orienteering in which instead of k we are given a budget B and the goal is to find a walk of length at most B starting at s that visits as many vertices as possible. In the point-to-point orienteering (P2P orienteering) we are given start and end nodes s,t and the walk is supposed to start at s and end at t. In the deadline TSP (which generalizes P2P orienteering) we are given a deadline D(v) for each v ∈ V and the goal is to find a walk starting at s that visits as many vertices as possible before their deadline (where the visit time of a node is the distance travelled from s to that node). The best approximation for rooted orienteering (or P2P orienteering) is (2+ε)-approximation [Chekuri et al., 2012] and O(log n)-approximation for deadline TSP [Nikhil Bansal et al., 2004]. For Euclidean metrics of fixed dimension, Chen and Har-Peled present [Chen and Har-Peled, 2008] a PTAS for rooted orienteering. There is no known approximation scheme for deadline TSP for any metric (not even trees). Our main result is the first approximation scheme for deadline TSP on metrics with bounded doubling dimension (which includes Euclidean metrics). To do so we first we present a quasi-polynomial time approximation scheme for k-path and P2P orienteering on such metrics. More specifically, if G is a metric with doubling dimension κ and aspect ratio Δ, we present a (1+ε)-approximation that runs in time n^{O((logΔ/ε) ^{2κ+1})}. Building upon these, we obtain an approximation scheme for deadline TSP when the distances and deadlines are integer which runs in time n^{O((log Δ/ε) ^{2κ+2})}. The same approach also implies a bicriteria (1+ε,1+ε)-approximation for deadline TSP for when distances and deadlines are in ℚ^+. For graphs with bounded treewidth ω we show how to solve k-path and P2P orienteering exactly in polynomial time and a (1+ε)-approximation for deadline TSP in time n^O((ωlogΔ/ε)²).
Cite as

Kinter Ren and Mohammad R. Salavatipour. Approximation Schemes for Orienteering and Deadline TSP in Doubling Metrics. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 1:1-1:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ren_et_al:LIPIcs.APPROX/RANDOM.2025.1,
  author =	{Ren, Kinter and Salavatipour, Mohammad R.},
  title =	{{Approximation Schemes for Orienteering and Deadline TSP in Doubling Metrics}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{1:1--1:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.1},
  URN =		{urn:nbn:de:0030-drops-243678},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.1},
  annote =	{Keywords: Deadline Traveling Salesman Problem, Orienteering, Doubling Metrics, Approximation algorithm}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.27
Computing Oriented Spanners and Their Dilation

Authors: Kevin Buchin, Antonia Kalb, Anil Maheshwari, Saeed Odak, Carolin Rehs, Michiel Smid, and Sampson Wong

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
Given a point set P in a metric space and a real number t ≥ 1, an oriented t-spanner is an oriented graph G = (P, E), where for every pair of distinct points p and q in P, the shortest oriented closed walk in G that contains p and q is at most a factor t longer than the perimeter of the smallest triangle in P containing p and q. The oriented dilation of a graph G is the minimum t for which G is an oriented t-spanner. For arbitrary point sets of size n in ℝ^d, where d ≥ 2 is a constant, the only known oriented spanner construction is an oriented 2-spanner with binom(n,2) edges. Moreover, there exists a set P of four points in the plane, for which the oriented dilation is larger than 1.46, for any oriented graph on P. We present the first algorithm that computes, in Euclidean space, a sparse oriented spanner whose oriented dilation is bounded by a constant. More specifically, for any set of n points in ℝ^d, where d is a constant, we construct an oriented (2+ε)-spanner with 𝒪(n) edges in 𝒪(n log n) time and 𝒪(n) space. Our construction uses the well-separated pair decomposition and an algorithm that computes a (1+ε)-approximation of the minimum-perimeter triangle in P containing two given query points in 𝒪(log n) time. While our algorithm is based on first computing a suitable undirected graph and then orienting it, we show that, in general, computing the orientation of an undirected graph that minimises its oriented dilation is NP-hard, even for point sets in the Euclidean plane. We further prove that even if the oriented graph is already given, computing its oriented dilation is APSP-hard for points in a general metric space. We complement this result with an algorithm that approximates the oriented dilation of a given graph in subcubic time for point sets in ℝ^d, where d is a constant.
Cite as

Kevin Buchin, Antonia Kalb, Anil Maheshwari, Saeed Odak, Carolin Rehs, Michiel Smid, and Sampson Wong. Computing Oriented Spanners and Their Dilation. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 27:1-27:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{buchin_et_al:LIPIcs.SoCG.2025.27,
  author =	{Buchin, Kevin and Kalb, Antonia and Maheshwari, Anil and Odak, Saeed and Rehs, Carolin and Smid, Michiel and Wong, Sampson},
  title =	{{Computing Oriented Spanners and Their Dilation}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{27:1--27:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.27},
  URN =		{urn:nbn:de:0030-drops-231792},
  doi =		{10.4230/LIPIcs.SoCG.2025.27},
  annote =	{Keywords: spanner, oriented graph, dilation, orientation, well-separated pair decomposition, minimum-perimeter triangle}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.77
Dynamic Maximum Depth of Geometric Objects

Authors: Subhash Suri, Jie Xue, Xiongxin Yang, and Jiumu Zhu

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
Given a set of geometric objects in the plane (rectangles, squares, disks etc.), its maximum depth (or geometric clique) is the largest number of objects with a common intersection. In this paper, we present data structures for dynamically maintaining the maximum depth under insertions and deletions of geometric objects, with sublinear update time. We achieve the following results: - a 1/k-approximate dynamic maximum-depth data structure for (axis-parallel) rectangles with O(n^{1/(k+1)} log n) amortized update time, for any fixed k ∈ ℤ^+. In particular, when k = 1, this gives an exact data structure for rectangles with O(√n log n) amortized update time, almost matching the best known bound for the offline version of the problem. - a (1/2-ε)-approximate dynamic maximum-depth data structure for disks with n^{2/3} log^{O(1)}n amortized update time, for any constant ε > 0. Having exact data structures for disks with sublinear update time is unlikely, since the static maximum-depth problem for disks is 3SUM-hard and thus does not admit subquadratic-time algorithms.
Cite as

Subhash Suri, Jie Xue, Xiongxin Yang, and Jiumu Zhu. Dynamic Maximum Depth of Geometric Objects. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 77:1-77:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{suri_et_al:LIPIcs.SoCG.2025.77,
  author =	{Suri, Subhash and Xue, Jie and Yang, Xiongxin and Zhu, Jiumu},
  title =	{{Dynamic Maximum Depth of Geometric Objects}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{77:1--77:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.77},
  URN =		{urn:nbn:de:0030-drops-232295},
  doi =		{10.4230/LIPIcs.SoCG.2025.77},
  annote =	{Keywords: dynamic algorithms, maximum depth}
}
Document
CG Challenge
DOI: 10.4230/LIPIcs.SoCG.2024.83
Computing Maximum Polygonal Packings in Convex Polygons Using Best-Fit, Genetic Algorithms and ILPs (CG Challenge)

Authors: Alkan Atak, Kevin Buchin, Mart Hagedoorn, Jona Heinrichs, Karsten Hogreve, Guangping Li, and Patrick Pawelczyk

Published in: LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024)

Abstract
Given a convex region P and a set of irregular polygons with associated profits, the Maximum Polygon Packing Problem seeks a non-overlapping packing of a subset of the polygons (without rotations) into P maximizing the profit of the packed polygons. Depending on the size of an instance, we use different algorithmic solutions: integer linear programs for small instances, genetic algorithms for medium-sized instances and a best-fit approach for large instances. For packing rectilinear polygons we provide a dedicated best-fit algorithm.
Cite as

Alkan Atak, Kevin Buchin, Mart Hagedoorn, Jona Heinrichs, Karsten Hogreve, Guangping Li, and Patrick Pawelczyk. Computing Maximum Polygonal Packings in Convex Polygons Using Best-Fit, Genetic Algorithms and ILPs (CG Challenge). In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 83:1-83:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{atak_et_al:LIPIcs.SoCG.2024.83,
  author =	{Atak, Alkan and Buchin, Kevin and Hagedoorn, Mart and Heinrichs, Jona and Hogreve, Karsten and Li, Guangping and Pawelczyk, Patrick},
  title =	{{Computing Maximum Polygonal Packings in Convex Polygons Using Best-Fit, Genetic Algorithms and ILPs}},
  booktitle =	{40th International Symposium on Computational Geometry (SoCG 2024)},
  pages =	{83:1--83:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-316-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{293},
  editor =	{Mulzer, Wolfgang and Phillips, Jeff M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.83},
  URN =		{urn:nbn:de:0030-drops-200283},
  doi =		{10.4230/LIPIcs.SoCG.2024.83},
  annote =	{Keywords: Polygon Packing, Nesting Problem, Genetic Algorithm, Integer Linear Programming}
}
Document
DOI: 10.4230/LIPIcs.GIScience.2023.2
Transitions in Dynamic Point Labeling

Authors: Thomas Depian, Guangping Li, Martin Nöllenburg, and Jules Wulms

Published in: LIPIcs, Volume 277, 12th International Conference on Geographic Information Science (GIScience 2023)

Abstract
The labeling of point features on a map is a well-studied topic. In a static setting, the goal is to find a non-overlapping label placement for (a subset of) point features. In a dynamic setting, the set of point features and their corresponding labels change, and the labeling has to adapt to such changes. To aid the user in tracking these changes, we can use morphs, here called transitions, to indicate how a labeling changes. Such transitions have not gained much attention yet, and we investigate different types of transitions for labelings of points, most notably consecutive transitions and simultaneous transitions. We give (tight) bounds on the number of overlaps that can occur during these transitions. When each label has a (non-negative) weight associated to it, and each overlap imposes a penalty proportional to the weight of the overlapping labels, we show that it is NP-complete to decide whether the penalty during a simultaneous transition has weight at most k. Finally, in a case study, we consider geotagged Twitter data on a map, by labeling points with rectangular labels showing tweets. We developed a prototype implementation to evaluate different transition styles in practice, measuring both number of overlaps and transition duration.
Cite as

Thomas Depian, Guangping Li, Martin Nöllenburg, and Jules Wulms. Transitions in Dynamic Point Labeling. In 12th International Conference on Geographic Information Science (GIScience 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 277, pp. 2:1-2:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{depian_et_al:LIPIcs.GIScience.2023.2,
  author =	{Depian, Thomas and Li, Guangping and N\"{o}llenburg, Martin and Wulms, Jules},
  title =	{{Transitions in Dynamic Point Labeling}},
  booktitle =	{12th International Conference on Geographic Information Science (GIScience 2023)},
  pages =	{2:1--2:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-288-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{277},
  editor =	{Beecham, Roger and Long, Jed A. and Smith, Dianna and Zhao, Qunshan and Wise, Sarah},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GIScience.2023.2},
  URN =		{urn:nbn:de:0030-drops-188971},
  doi =		{10.4230/LIPIcs.GIScience.2023.2},
  annote =	{Keywords: Dynamic labels, Label overlaps, Morphs, NP-completeness, Case study}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.19
Untangling Circular Drawings: Algorithms and Complexity

Authors: Sujoy Bhore, Guangping Li, Martin Nöllenburg, Ignaz Rutter, and Hsiang-Yun Wu

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
We consider the problem of untangling a given (non-planar) straight-line circular drawing δ_G of an outerplanar graph G = (V,E) into a planar straight-line circular drawing by shifting a minimum number of vertices to a new position on the circle. For an outerplanar graph G, it is clear that such a crossing-free circular drawing always exists and we define the circular shifting number shift°(δ_G) as the minimum number of vertices that need to be shifted to resolve all crossings of δ_G. We show that the problem Circular Untangling, asking whether shift°(δ_G) ≤ K for a given integer K, is NP-complete. Based on this result we study Circular Untangling for almost-planar circular drawings, in which a single edge is involved in all the crossings. In this case we provide a tight upper bound shift°(δ_G) ≤ ⌊n/2⌋-1, where n is the number of vertices in G, and present a polynomial-time algorithm to compute the circular shifting number of almost-planar drawings.
Cite as

Sujoy Bhore, Guangping Li, Martin Nöllenburg, Ignaz Rutter, and Hsiang-Yun Wu. Untangling Circular Drawings: Algorithms and Complexity. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 19:1-19:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bhore_et_al:LIPIcs.ISAAC.2021.19,
  author =	{Bhore, Sujoy and Li, Guangping and N\"{o}llenburg, Martin and Rutter, Ignaz and Wu, Hsiang-Yun},
  title =	{{Untangling Circular Drawings: Algorithms and Complexity}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{19:1--19:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.19},
  URN =		{urn:nbn:de:0030-drops-154528},
  doi =		{10.4230/LIPIcs.ISAAC.2021.19},
  annote =	{Keywords: graph drawing, straight-line drawing, outerplanarity, NP-hardness, untangling}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.19
An Algorithmic Study of Fully Dynamic Independent Sets for Map Labeling

Authors: Sujoy Bhore, Guangping Li, and Martin Nöllenburg

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
Map labeling is a classical problem in cartography and geographic information systems (GIS) that asks to place labels for area, line, and point features, with the goal to select and place the maximum number of independent, i.e., overlap-free, labels. A practically interesting case is point labeling with axis-parallel rectangular labels of common size. In a fully dynamic setting, at each time step, either a new label appears or an existing label disappears. Then, the challenge is to maintain a maximum cardinality subset of pairwise independent labels with sub-linear update time. Motivated by this, we study the maximal independent set (MIS) and maximum independent set (Max-IS) problems on fully dynamic (insertion/deletion model) sets of axis-parallel rectangles of two types - (i) uniform height and width and (ii) uniform height and arbitrary width; both settings can be modeled as rectangle intersection graphs. We present the first deterministic algorithm for maintaining a MIS (and thus a 4-approximate Max-IS) of a dynamic set of uniform rectangles with amortized sub-logarithmic update time. This breaks the natural barrier of Ω(Δ) update time (where Δ is the maximum degree in the graph) for vertex updates presented by Assadi et al. (STOC 2018). We continue by investigating Max-IS and provide a series of deterministic dynamic approximation schemes. For uniform rectangles, we first give an algorithm that maintains a 4-approximate Max-IS with O(1) update time. In a subsequent algorithm, we establish the trade-off between approximation quality 2(1+1/k) and update time O(k²log n), for k ∈ ℕ. We conclude with an algorithm that maintains a 2-approximate Max-IS for dynamic sets of unit-height and arbitrary-width rectangles with O(ω log n) update time, where ω is the maximum size of an independent set of rectangles stabbed by any horizontal line. We have implemented our algorithms and report the results of an experimental comparison exploring the trade-off between solution quality and update time for synthetic and real-world map labeling instances.
Cite as

Sujoy Bhore, Guangping Li, and Martin Nöllenburg. An Algorithmic Study of Fully Dynamic Independent Sets for Map Labeling. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 19:1-19:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bhore_et_al:LIPIcs.ESA.2020.19,
  author =	{Bhore, Sujoy and Li, Guangping and N\"{o}llenburg, Martin},
  title =	{{An Algorithmic Study of Fully Dynamic Independent Sets for Map Labeling}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{19:1--19:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.19},
  URN =		{urn:nbn:de:0030-drops-128856},
  doi =		{10.4230/LIPIcs.ESA.2020.19},
  annote =	{Keywords: Independent Sets, Dynamic Algorithms, Rectangle Intersection Graphs, Approximation Algorithms, Experimental Evaluation}
}
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