18 Search Results for "Chang, Hsien-Chih"

Document
DOI: 10.4230/OASIcs.ICPEC.2024.11
Client-Side Gamification Engine for Enhanced Programming Learning

Authors: Ricardo Queirós, Robertas Damaševičius, Rytis Maskeliūnas, and Jakub Swacha

Published in: OASIcs, Volume 122, 5th International Computer Programming Education Conference (ICPEC 2024)

Abstract
This study introduces the development of a client-based software layer within the FGPE project, aimed at enhancing the usability of the FGPE programming learning environment through client-side processing. The primary goal is to enable the evaluation of programming exercises and the application of gamification rules directly on the client-side, thereby facilitating offline functionality. This approach is particularly beneficial in regions with unreliable internet connectivity, as it allows continuous student interaction and feedback without the need for a constant server connection. The implementation promises to reduce server load significantly by shifting the evaluation workload to the client-side. This not only improves response times but also alleviates the burden on server resources, enhancing overall system efficiency. Two main strategies are explored: 1) caching the gamification service interface on the client-side, and 2) implementing a complete client-side gamification service that synchronizes with the server when online. Each approach is evaluated in terms of its impact on user experience, system performance, and potential security concerns. The findings suggest that while client-side processing offers considerable benefits in terms of scalability and user engagement, it also introduces challenges such as increased system complexity and potential data synchronization issues. The study concludes with recommendations for balancing these factors to optimize the design and implementation of client-based systems for educational environments.
Cite as

Ricardo Queirós, Robertas Damaševičius, Rytis Maskeliūnas, and Jakub Swacha. Client-Side Gamification Engine for Enhanced Programming Learning. In 5th International Computer Programming Education Conference (ICPEC 2024). Open Access Series in Informatics (OASIcs), Volume 122, pp. 11:1-11:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{queiros_et_al:OASIcs.ICPEC.2024.11,
  author =	{Queir\'{o}s, Ricardo and Dama\v{s}evi\v{c}ius, Robertas and Maskeli\={u}nas, Rytis and Swacha, Jakub},
  title =	{{Client-Side Gamification Engine for Enhanced Programming Learning}},
  booktitle =	{5th International Computer Programming Education Conference (ICPEC 2024)},
  pages =	{11:1--11:12},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-347-8},
  ISSN =	{2190-6807},
  year =	{2024},
  volume =	{122},
  editor =	{Santos, Andr\'{e} L. and Pinto-Albuquerque, Maria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ICPEC.2024.11},
  URN =		{urn:nbn:de:0030-drops-209809},
  doi =		{10.4230/OASIcs.ICPEC.2024.11},
  annote =	{Keywords: Code generation, Computer Programming, Gamification}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.50
Making Multicurves Cross Minimally on Surfaces

Authors: Loïc Dubois

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
On an orientable surface S, consider a collection Γ of closed curves. The (geometric) intersection number i_S(Γ) is the minimum number of self-intersections that a collection Γ' can have, where Γ' results from a continuous deformation (homotopy) of Γ. We provide algorithms that compute i_S(Γ) and such a Γ', assuming that Γ is given by a collection of closed walks of length n in a graph M cellularly embedded on S, in O(n log n) time when M and S are fixed. The state of the art is a paper of Despré and Lazarus [SoCG 2017, J. ACM 2019], who compute i_S(Γ) in O(n²) time, and Γ' in O(n⁴) time if Γ is a single closed curve. Our result is more general since we can put an arbitrary number of closed curves in minimal position. Also, our algorithms are quasi-linear in n instead of quadratic and quartic. Most importantly, our proofs are simpler, shorter, and more structured. We use techniques from two-dimensional topology and from the theory of hyperbolic surfaces. Most notably, we prove a new property of the reducing triangulations introduced by Colin de Verdière, Despré, and Dubois [SODA 2024], reducing our problem to the case of surfaces with boundary. As a key subroutine, we rely on an algorithm of Fulek and Tóth [JCO 2020].
Cite as

Loïc Dubois. Making Multicurves Cross Minimally on Surfaces. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 50:1-50:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dubois:LIPIcs.ESA.2024.50,
  author =	{Dubois, Lo\"{i}c},
  title =	{{Making Multicurves Cross Minimally on Surfaces}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{50:1--50:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.50},
  URN =		{urn:nbn:de:0030-drops-211216},
  doi =		{10.4230/LIPIcs.ESA.2024.50},
  annote =	{Keywords: Algorithms, Topology, Surfaces, Closed Curves, Geometric Intersection Number}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.51
Better Diameter Algorithms for Bounded VC-Dimension Graphs and Geometric Intersection Graphs

Authors: Lech Duraj, Filip Konieczny, and Krzysztof Potępa

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
We develop a framework for algorithms finding the diameter in graphs of bounded distance Vapnik-Chervonenkis dimension, in (parameterized) subquadratic time complexity. The class of bounded distance VC-dimension graphs is wide, including, e.g. all minor-free graphs. We build on the work of Ducoffe et al. [SODA'20, SIGCOMP'22], improving their technique. With our approach the algorithms become simpler and faster, working in 𝒪{(k ⋅ n^{1-1/d} ⋅ m ⋅ polylog(n))} time complexity for the graph on n vertices and m edges, where k is the diameter and d is the distance VC-dimension of the graph. Furthermore, it allows us to use the improved technique in more general setting. In particular, we use this framework for geometric intersection graphs, i.e. graphs where vertices are identical geometric objects on a plane and the adjacency is defined by intersection. Applying our approach for these graphs, we partially answer a question posed by Bringmann et al. [SoCG'22], finding an 𝒪{(n^{7/4} ⋅ polylog(n))} parameterized diameter algorithm for unit square intersection graph of size n, as well as a more general algorithm for convex polygon intersection graphs.
Cite as

Lech Duraj, Filip Konieczny, and Krzysztof Potępa. Better Diameter Algorithms for Bounded VC-Dimension Graphs and Geometric Intersection Graphs. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 51:1-51:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{duraj_et_al:LIPIcs.ESA.2024.51,
  author =	{Duraj, Lech and Konieczny, Filip and Pot\k{e}pa, Krzysztof},
  title =	{{Better Diameter Algorithms for Bounded VC-Dimension Graphs and Geometric Intersection Graphs}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{51:1--51:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.51},
  URN =		{urn:nbn:de:0030-drops-211229},
  doi =		{10.4230/LIPIcs.ESA.2024.51},
  annote =	{Keywords: Graph Diameter, Geometric Intersection Graphs, Vapnik-Chervonenkis Dimension}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.66
Shortest Path Separators in Unit Disk Graphs

Authors: Elfarouk Harb, Zhengcheng Huang, and Da Wei Zheng

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
We introduce a new balanced separator theorem for unit-disk graphs involving two shortest paths combined with the 1-hop neighbours of those paths and two other vertices. This answers an open problem of Yan, Xiang and Dragan [CGTA '12] and improves their result that requires removing the 3-hop neighbourhood of two shortest paths. Our proof uses very different ideas, including Delaunay triangulations and a generalization of the celebrated balanced separator theorem of Lipton and Tarjan [J. Appl. Math. '79] to systems of non-intersecting paths.
Cite as

Elfarouk Harb, Zhengcheng Huang, and Da Wei Zheng. Shortest Path Separators in Unit Disk Graphs. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 66:1-66:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{harb_et_al:LIPIcs.ESA.2024.66,
  author =	{Harb, Elfarouk and Huang, Zhengcheng and Zheng, Da Wei},
  title =	{{Shortest Path Separators in Unit Disk Graphs}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{66:1--66:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.66},
  URN =		{urn:nbn:de:0030-drops-211375},
  doi =		{10.4230/LIPIcs.ESA.2024.66},
  annote =	{Keywords: Balanced shortest path separators, unit disk graphs, crossings}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.69
PHOBIC: Perfect Hashing With Optimized Bucket Sizes and Interleaved Coding

Authors: Stefan Hermann, Hans-Peter Lehmann, Giulio Ermanno Pibiri, Peter Sanders, and Stefan Walzer

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
A minimal perfect hash function (or MPHF) maps a set of n keys to [n] : = {1, …, n} without collisions. Such functions find widespread application e.g. in bioinformatics and databases. In this paper we revisit PTHash - a construction technique particularly designed for fast queries. PTHash distributes the input keys into small buckets and, for each bucket, it searches for a hash function seed that places its keys in the output domain without collisions. The collection of all seeds is then stored in a compressed way. Since the first buckets are easier to place, buckets are considered in non-increasing order of size. Additionally, PTHash heuristically produces an imbalanced distribution of bucket sizes by distributing 60% of the keys into 30% of the buckets. Our main contribution is to characterize, up to lower order terms, an optimal choice for the expected bucket sizes, improving construction throughput for space efficient configurations both in theory and practice. Further contributions include a new encoding scheme for seeds that works across partitions of the data structure and a GPU parallelization. Compared to PTHash, PHOBIC is 0.17 bits/key more space efficient for same query time and construction throughput. For a configuration with fast queries, our GPU implementation can construct an MPHF at 2.17 bits/key in 28 ns/key, which can be queried in 37 ns/query on the CPU.
Cite as

Stefan Hermann, Hans-Peter Lehmann, Giulio Ermanno Pibiri, Peter Sanders, and Stefan Walzer. PHOBIC: Perfect Hashing With Optimized Bucket Sizes and Interleaved Coding. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 69:1-69:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hermann_et_al:LIPIcs.ESA.2024.69,
  author =	{Hermann, Stefan and Lehmann, Hans-Peter and Pibiri, Giulio Ermanno and Sanders, Peter and Walzer, Stefan},
  title =	{{PHOBIC: Perfect Hashing With Optimized Bucket Sizes and Interleaved Coding}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{69:1--69:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.69},
  URN =		{urn:nbn:de:0030-drops-211405},
  doi =		{10.4230/LIPIcs.ESA.2024.69},
  annote =	{Keywords: Compressed Data Structures, Minimal Perfect Hashing, GPU}
}
Document
DOI: 10.4230/LIPIcs.AofA.2024.8
Galled Tree-Child Networks

Authors: Yu-Sheng Chang, Michael Fuchs, and Guan-Ru Yu

Published in: LIPIcs, Volume 302, 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)

Abstract
We propose the class of galled tree-child networks which is obtained as intersection of the classes of galled networks and tree-child networks. For the latter two classes, (asymptotic) counting results and stochastic results have been proved with very different methods. We show that a counting result for the class of galled tree-child networks follows with similar tools as used for galled networks, however, the result has a similar pattern as the one for tree-child networks. In addition, we also consider the (suitably scaled) numbers of reticulation nodes of random galled tree-child networks and show that they are asymptotically normal distributed. This is in contrast to the limit laws of the corresponding quantities for galled networks and tree-child networks which have been both shown to be discrete.
Cite as

Yu-Sheng Chang, Michael Fuchs, and Guan-Ru Yu. Galled Tree-Child Networks. In 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 8:1-8:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chang_et_al:LIPIcs.AofA.2024.8,
  author =	{Chang, Yu-Sheng and Fuchs, Michael and Yu, Guan-Ru},
  title =	{{Galled Tree-Child Networks}},
  booktitle =	{35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)},
  pages =	{8:1--8:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-329-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{302},
  editor =	{Mailler, C\'{e}cile and Wild, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2024.8},
  URN =		{urn:nbn:de:0030-drops-204439},
  doi =		{10.4230/LIPIcs.AofA.2024.8},
  annote =	{Keywords: Phylogenetic Network, galled Network, tree-child Network, asymptotic Enumeration, Limit Law, Lagrange Inversion}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.27
The Discrepancy of Shortest Paths

Authors: Greg Bodwin, Chengyuan Deng, Jie Gao, Gary Hoppenworth, Jalaj Upadhyay, and Chen Wang

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
The hereditary discrepancy of a set system is a quantitative measure of the pseudorandom properties of the system. Roughly speaking, hereditary discrepancy measures how well one can 2-color the elements of the system so that each set contains approximately the same number of elements of each color. Hereditary discrepancy has numerous applications in computational geometry, communication complexity and derandomization. More recently, the hereditary discrepancy of the set system of shortest paths has found applications in differential privacy [Chen et al. SODA 23]. The contribution of this paper is to improve the upper and lower bounds on the hereditary discrepancy of set systems of unique shortest paths in graphs. In particular, we show that any system of unique shortest paths in an undirected weighted graph has hereditary discrepancy O(n^{1/4}), and we construct lower bound examples demonstrating that this bound is tight up to polylog n factors. Our lower bounds hold even for planar graphs and bipartite graphs, and improve a previous lower bound of Ω(n^{1/6}) obtained by applying the trace bound of Chazelle and Lvov [SoCG'00] to a classical point-line system of Erdős. As applications, we improve the lower bound on the additive error for differentially-private all pairs shortest distances from Ω(n^{1/6}) [Chen et al. SODA 23] to Ω̃(n^{1/4}), and we improve the lower bound on additive error for the differentially-private all sets range queries problem to Ω̃(n^{1/4}), which is tight up to polylog n factors [Deng et al. WADS 23].
Cite as

Greg Bodwin, Chengyuan Deng, Jie Gao, Gary Hoppenworth, Jalaj Upadhyay, and Chen Wang. The Discrepancy of Shortest Paths. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 27:1-27:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bodwin_et_al:LIPIcs.ICALP.2024.27,
  author =	{Bodwin, Greg and Deng, Chengyuan and Gao, Jie and Hoppenworth, Gary and Upadhyay, Jalaj and Wang, Chen},
  title =	{{The Discrepancy of Shortest Paths}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{27:1--27:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.27},
  URN =		{urn:nbn:de:0030-drops-201705},
  doi =		{10.4230/LIPIcs.ICALP.2024.27},
  annote =	{Keywords: Discrepancy, hereditary discrepancy, shortest paths, differential privacy}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2024.37
Optimal Euclidean Tree Covers

Authors: Hsien-Chih Chang, Jonathan Conroy, Hung Le, Lazar Milenković, Shay Solomon, and Cuong Than

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

Abstract
A (1+e)-stretch tree cover of a metric space is a collection of trees, where every pair of points has a (1+e)-stretch path in one of the trees. The celebrated Dumbbell Theorem [Arya et al. STOC'95] states that any set of n points in d-dimensional Euclidean space admits a (1+e)-stretch tree cover with O_d(e^{-d} ⋅ log(1/e)) trees, where the O_d notation suppresses terms that depend solely on the dimension d. The running time of their construction is O_d(n log n ⋅ log(1/e)/e^d + n ⋅ e^{-2d}). Since the same point may occur in multiple levels of the tree, the maximum degree of a point in the tree cover may be as large as Ω(log Φ), where Φ is the aspect ratio of the input point set. In this work we present a (1+e)-stretch tree cover with O_d(e^{-d+1} ⋅ log(1/e)) trees, which is optimal (up to the log(1/e) factor). Moreover, the maximum degree of points in any tree is an absolute constant for any d. As a direct corollary, we obtain an optimal {routing scheme} in low-dimensional Euclidean spaces. We also present a (1+e)-stretch Steiner tree cover (that may use Steiner points) with O_d(e^{(-d+1)/2} ⋅ log(1/e)) trees, which too is optimal. The running time of our two constructions is linear in the number of edges in the respective tree covers, ignoring an additive O_d(n log n) term; this improves over the running time underlying the Dumbbell Theorem.
Cite as

Hsien-Chih Chang, Jonathan Conroy, Hung Le, Lazar Milenković, Shay Solomon, and Cuong Than. Optimal Euclidean Tree Covers. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 37:1-37:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chang_et_al:LIPIcs.SoCG.2024.37,
  author =	{Chang, Hsien-Chih and Conroy, Jonathan and Le, Hung and Milenkovi\'{c}, Lazar and Solomon, Shay and Than, Cuong},
  title =	{{Optimal Euclidean Tree Covers}},
  booktitle =	{40th International Symposium on Computational Geometry (SoCG 2024)},
  pages =	{37:1--37:15},
  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.2024.37},
  URN =		{urn:nbn:de:0030-drops-199828},
  doi =		{10.4230/LIPIcs.SoCG.2024.37},
  annote =	{Keywords: Tree cover, spanner, Steiner point, routing, bounded-degree, quadtree, net-tree}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2024.38
Computing Diameter+2 in Truly-Subquadratic Time for Unit-Disk Graphs

Authors: Hsien-Chih Chang, Jie Gao, and Hung Le

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

Abstract
Finding the diameter of a graph in general cannot be done in truly subquadratic assuming the Strong Exponential Time Hypothesis (SETH), even when the underlying graph is unweighted and sparse. When restricting to concrete classes of graphs and assuming SETH, planar graphs and minor-free graphs admit truly subquadratic algorithms, while geometric intersection graphs of unit balls, congruent equilateral triangles, and unit segments do not. Unit-disk graphs is one of the major open cases where the complexity of diameter computation remains unknown. More generally, it is conjectured that a truly subquadratic time algorithm exists for pseudo-disk graphs where each pair of objects has at most two intersections on the boundary. In this paper, we show a truly-subquadratic algorithm of running time O^~(n^{2-1/18}), for finding the diameter in a unit-disk graph, whose output differs from the optimal solution by at most 2. This is the first algorithm that provides an additive guarantee in distortion, independent of the size or the diameter of the graph. Our algorithm requires two important technical elements. First, we show that for the intersection graph of pseudo-disks, the graph VC-dimension - either of k-hop balls or the distance encoding vectors - is 4. This contrasts to the VC dimension of the pseudo-disks themselves as geometric ranges (which is known to be 3). Second, we introduce a clique-based r-clustering for geometric intersection graphs, which is an analog of the r-division construction for planar graphs. We also showcase the new techniques by establishing new results for distance oracles for unit-disk graphs with subquadratic storage and O(1) query time. The results naturally extend to unit L₁ or L_∞-disks and fat pseudo-disks of similar size. Last, if the pseudo-disks additionally have bounded ply, we have a truly subquadratic algorithm to find the exact diameter.
Cite as

Hsien-Chih Chang, Jie Gao, and Hung Le. Computing Diameter+2 in Truly-Subquadratic Time for Unit-Disk Graphs. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 38:1-38:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chang_et_al:LIPIcs.SoCG.2024.38,
  author =	{Chang, Hsien-Chih and Gao, Jie and Le, Hung},
  title =	{{Computing Diameter+2 in Truly-Subquadratic Time for Unit-Disk Graphs}},
  booktitle =	{40th International Symposium on Computational Geometry (SoCG 2024)},
  pages =	{38:1--38:14},
  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.2024.38},
  URN =		{urn:nbn:de:0030-drops-199833},
  doi =		{10.4230/LIPIcs.SoCG.2024.38},
  annote =	{Keywords: Unit-disk graph, pseudo-disks, r-division, VC-dimension, distance oracle, clique-based separator}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2020.8
Clustering Under Perturbation Stability in Near-Linear Time

Authors: Pankaj K. Agarwal, Hsien-Chih Chang, Kamesh Munagala, Erin Taylor, and Emo Welzl

Published in: LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)

Abstract
We consider the problem of center-based clustering in low-dimensional Euclidean spaces under the perturbation stability assumption. An instance is α-stable if the underlying optimal clustering continues to remain optimal even when all pairwise distances are arbitrarily perturbed by a factor of at most α. Our main contribution is in presenting efficient exact algorithms for α-stable clustering instances whose running times depend near-linearly on the size of the data set when α ≥ 2 + √3. For k-center and k-means problems, our algorithms also achieve polynomial dependence on the number of clusters, k, when α ≥ 2 + √3 + ε for any constant ε > 0 in any fixed dimension. For k-median, our algorithms have polynomial dependence on k for α > 5 in any fixed dimension; and for α ≥ 2 + √3 in two dimensions. Our algorithms are simple, and only require applying techniques such as local search or dynamic programming to a suitably modified metric space, combined with careful choice of data structures.
Cite as

Pankaj K. Agarwal, Hsien-Chih Chang, Kamesh Munagala, Erin Taylor, and Emo Welzl. Clustering Under Perturbation Stability in Near-Linear Time. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{agarwal_et_al:LIPIcs.FSTTCS.2020.8,
  author =	{Agarwal, Pankaj K. and Chang, Hsien-Chih and Munagala, Kamesh and Taylor, Erin and Welzl, Emo},
  title =	{{Clustering Under Perturbation Stability in Near-Linear Time}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{8:1--8:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Saxena, Nitin and Simon, Sunil},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.8},
  URN =		{urn:nbn:de:0030-drops-132492},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.8},
  annote =	{Keywords: clustering, stability, local search, dynamic programming, coreset, polyhedral metric, trapezoid decomposition, range query}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2020.2
Dynamic Geometric Set Cover and Hitting Set

Authors: Pankaj K. Agarwal, Hsien-Chih Chang, Subhash Suri, Allen Xiao, and Jie Xue

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
We investigate dynamic versions of geometric set cover and hitting set where points and ranges may be inserted or deleted, and we want to efficiently maintain an (approximately) optimal solution for the current problem instance. While their static versions have been extensively studied in the past, surprisingly little is known about dynamic geometric set cover and hitting set. For instance, even for the most basic case of one-dimensional interval set cover and hitting set, no nontrivial results were known. The main contribution of our paper are two frameworks that lead to efficient data structures for dynamically maintaining set covers and hitting sets in ℝ¹ and ℝ². The first framework uses bootstrapping and gives a (1+ε)-approximate data structure for dynamic interval set cover in ℝ¹ with O(n^α/ε) amortized update time for any constant α > 0; in ℝ², this method gives O(1)-approximate data structures for unit-square (and quadrant) set cover and hitting set with O(n^(1/2+α)) amortized update time. The second framework uses local modification, and leads to a (1+ε)-approximate data structure for dynamic interval hitting set in ℝ¹ with Õ(1/ε) amortized update time; in ℝ², it gives O(1)-approximate data structures for unit-square (and quadrant) set cover and hitting set in the partially dynamic settings with Õ(1) amortized update time.
Cite as

Pankaj K. Agarwal, Hsien-Chih Chang, Subhash Suri, Allen Xiao, and Jie Xue. Dynamic Geometric Set Cover and Hitting Set. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 2:1-2:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{agarwal_et_al:LIPIcs.SoCG.2020.2,
  author =	{Agarwal, Pankaj K. and Chang, Hsien-Chih and Suri, Subhash and Xiao, Allen and Xue, Jie},
  title =	{{Dynamic Geometric Set Cover and Hitting Set}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{2:1--2:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.2},
  URN =		{urn:nbn:de:0030-drops-121604},
  doi =		{10.4230/LIPIcs.SoCG.2020.2},
  annote =	{Keywords: Geometric set cover, Geometric hitting set, Dynamic data structures}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2020.45
A Near-Linear Time Approximation Scheme for Geometric Transportation with Arbitrary Supplies and Spread

Authors: Kyle Fox and Jiashuai Lu

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
The geometric transportation problem takes as input a set of points P in d-dimensional Euclidean space and a supply function μ : P → ℝ. The goal is to find a transportation map, a non-negative assignment τ : P × P → ℝ_{≥ 0} to pairs of points, so the total assignment leaving each point is equal to its supply, i.e., ∑_{r ∈ P} τ(q, r) - ∑_{p ∈ P} τ(p, q) = μ(q) for all points q ∈ P. The goal is to minimize the weighted sum of Euclidean distances for the pairs, ∑_{(p, q) ∈ P × P} τ(p, q) ⋅ ||q - p||₂. We describe the first algorithm for this problem that returns, with high probability, a (1 + ε)-approximation to the optimal transportation map in O(n poly(1 / ε) polylog n) time. In contrast to the previous best algorithms for this problem, our near-linear running time bound is independent of the spread of P and the magnitude of its real-valued supplies.
Cite as

Kyle Fox and Jiashuai Lu. A Near-Linear Time Approximation Scheme for Geometric Transportation with Arbitrary Supplies and Spread. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 45:1-45:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{fox_et_al:LIPIcs.SoCG.2020.45,
  author =	{Fox, Kyle and Lu, Jiashuai},
  title =	{{A Near-Linear Time Approximation Scheme for Geometric Transportation with Arbitrary Supplies and Spread}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{45:1--45:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.45},
  URN =		{urn:nbn:de:0030-drops-122034},
  doi =		{10.4230/LIPIcs.SoCG.2020.45},
  annote =	{Keywords: Transportation map, earth mover’s distance, shape matching, approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2019.81
Spectral Aspects of Symmetric Matrix Signings

Authors: Charles Carlson, Karthekeyan Chandrasekaran, Hsien-Chih Chang, Naonori Kakimura, and Alexandra Kolla

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

Abstract
The spectra of signed matrices have played a fundamental role in social sciences, graph theory, and control theory. In this work, we investigate the computational problems of finding symmetric signings of matrices with natural spectral properties. Our results are the following: 1) We characterize matrices that have an invertible signing: a symmetric matrix has an invertible symmetric signing if and only if the support graph of the matrix contains a perfect 2-matching. Further, we present an efficient algorithm to search for an invertible symmetric signing. 2) We use the above-mentioned characterization to give an algorithm to find a minimum increase in the support of a given symmetric matrix so that it has an invertible symmetric signing. 3) We show NP-completeness of the following problems: verifying whether a given matrix has a symmetric signing that is singular or has bounded eigenvalues. However, we also illustrate that the complexity could differ substantially for input matrices that are adjacency matrices of graphs. We use combinatorial techniques in addition to classic results from matching theory.
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Charles Carlson, Karthekeyan Chandrasekaran, Hsien-Chih Chang, Naonori Kakimura, and Alexandra Kolla. Spectral Aspects of Symmetric Matrix Signings. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 81:1-81:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{carlson_et_al:LIPIcs.MFCS.2019.81,
  author =	{Carlson, Charles and Chandrasekaran, Karthekeyan and Chang, Hsien-Chih and Kakimura, Naonori and Kolla, Alexandra},
  title =	{{Spectral Aspects of Symmetric Matrix Signings}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{81:1--81:13},
  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.2019.81},
  URN =		{urn:nbn:de:0030-drops-110258},
  doi =		{10.4230/LIPIcs.MFCS.2019.81},
  annote =	{Keywords: Spectral Graph Theory, Matrix Signing, Matchings}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2019.6
Efficient Algorithms for Geometric Partial Matching

Authors: Pankaj K. Agarwal, Hsien-Chih Chang, and Allen Xiao

Published in: LIPIcs, Volume 129, 35th International Symposium on Computational Geometry (SoCG 2019)

Abstract
Let A and B be two point sets in the plane of sizes r and n respectively (assume r <= n), and let k be a parameter. A matching between A and B is a family of pairs in A x B so that any point of A cup B appears in at most one pair. Given two positive integers p and q, we define the cost of matching M to be c(M) = sum_{(a, b) in M}||a-b||_p^q where ||*||_p is the L_p-norm. The geometric partial matching problem asks to find the minimum-cost size-k matching between A and B. We present efficient algorithms for geometric partial matching problem that work for any powers of L_p-norm matching objective: An exact algorithm that runs in O((n + k^2)polylog n) time, and a (1 + epsilon)-approximation algorithm that runs in O((n + k sqrt{k})polylog n * log epsilon^{-1}) time. Both algorithms are based on the primal-dual flow augmentation scheme; the main improvements involve using dynamic data structures to achieve efficient flow augmentations. With similar techniques, we give an exact algorithm for the planar transportation problem running in O(min{n^2, rn^{3/2}}polylog n) time.
Cite as

Pankaj K. Agarwal, Hsien-Chih Chang, and Allen Xiao. Efficient Algorithms for Geometric Partial Matching. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 6:1-6:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{agarwal_et_al:LIPIcs.SoCG.2019.6,
  author =	{Agarwal, Pankaj K. and Chang, Hsien-Chih and Xiao, Allen},
  title =	{{Efficient Algorithms for Geometric Partial Matching}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{6:1--6:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Barequet, Gill and Wang, Yusu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2019.6},
  URN =		{urn:nbn:de:0030-drops-104109},
  doi =		{10.4230/LIPIcs.SoCG.2019.6},
  annote =	{Keywords: partial matching, transportation, optimal transport, minimum-cost flow, bichromatic closest pair}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2019.25
Lower Bounds for Electrical Reduction on Surfaces

Authors: Hsien-Chih Chang, Marcos Cossarini, and Jeff Erickson

Published in: LIPIcs, Volume 129, 35th International Symposium on Computational Geometry (SoCG 2019)

Abstract
We strengthen the connections between electrical transformations and homotopy from the planar setting - observed and studied since Steinitz - to arbitrary surfaces with punctures. As a result, we improve our earlier lower bound on the number of electrical transformations required to reduce an n-vertex graph on surface in the worst case [SOCG 2016] in two different directions. Our previous Omega(n^{3/2}) lower bound applies only to facial electrical transformations on plane graphs with no terminals. First we provide a stronger Omega(n^2) lower bound when the planar graph has two or more terminals, which follows from a quadratic lower bound on the number of homotopy moves in the annulus. Our second result extends our earlier Omega(n^{3/2}) lower bound to the wider class of planar electrical transformations, which preserve the planarity of the graph but may delete cycles that are not faces of the given embedding. This new lower bound follow from the observation that the defect of the medial graph of a planar graph is the same for all its planar embeddings.
Cite as

Hsien-Chih Chang, Marcos Cossarini, and Jeff Erickson. Lower Bounds for Electrical Reduction on Surfaces. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 25:1-25:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chang_et_al:LIPIcs.SoCG.2019.25,
  author =	{Chang, Hsien-Chih and Cossarini, Marcos and Erickson, Jeff},
  title =	{{Lower Bounds for Electrical Reduction on Surfaces}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{25:1--25:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Barequet, Gill and Wang, Yusu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2019.25},
  URN =		{urn:nbn:de:0030-drops-104294},
  doi =		{10.4230/LIPIcs.SoCG.2019.25},
  annote =	{Keywords: electrical transformation, Delta-Y-transformation, homotopy, tight, defect, SPQR-tree, smoothings, routing set, 2-flipping}
}
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