4 Search Results for "Brankovic, Milutin"

Document
DOI: 10.4230/LIPIcs.ESA.2025.84
Property Testing of Curve Similarity

Authors: Peyman Afshani, Maike Buchin, Anne Driemel, Marena Richter, and Sampson Wong

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We propose sublinear algorithms for probabilistic testing of the discrete and continuous Fréchet distance - a standard similarity measure for curves. We assume the algorithm is given access to the input curves via a query oracle: a query returns the set of vertices of the curve that lie within a radius δ of a specified vertex of the other curve. The goal is to use a small number of queries to determine with constant probability whether the two curves are similar (i.e., their discrete Fréchet distance is at most δ) or they are "ε-far" (for 0 < ε < 2) from being similar, i.e., more than an ε-fraction of the two curves must be ignored for them to become similar. We present two algorithms which are sublinear assuming that the curves are t-approximate shortest paths in the ambient metric space, for some t ≪ n. The first algorithm uses O(t/ε log t/ε) queries and is given the value of t in advance. The second algorithm does not have explicit knowledge of the value of t and therefore needs to gain implicit knowledge of the straightness of the input curves through its queries. We show that the discrete Fréchet distance can still be tested using roughly O({t³+t² log n}/ε) queries ignoring logarithmic factors in t. Our algorithms work in a matrix representation of the input and may be of independent interest to matrix testing. Our algorithms use a mild uniform sampling condition that constrains the edge lengths of the curves, similar to a polynomially bounded aspect ratio. Applied to testing the continuous Fréchet distance of t-straight curves, our algorithms can be used for (1+ε')-approximate testing using essentially the same bounds as stated above with an additional factor of poly(1/(ε')).
Cite as

Peyman Afshani, Maike Buchin, Anne Driemel, Marena Richter, and Sampson Wong. Property Testing of Curve Similarity. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 84:1-84:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{afshani_et_al:LIPIcs.ESA.2025.84,
  author =	{Afshani, Peyman and Buchin, Maike and Driemel, Anne and Richter, Marena and Wong, Sampson},
  title =	{{Property Testing of Curve Similarity}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{84:1--84:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.84},
  URN =		{urn:nbn:de:0030-drops-245522},
  doi =		{10.4230/LIPIcs.ESA.2025.84},
  annote =	{Keywords: Fr\'{e}chet distance, Trajectory Analysis, Curve Similarity, Property Testing, Monotonicity Testing}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.47
B-Treaps Revised: Write Efficient Randomized Block Search Trees with High Load

Authors: Roodabeh Safavi and Martin P. Seybold

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
Uniquely represented (UR) data structures represent each logical state with a unique storage state. We study the problem of maintaining a dynamic set of n keys from a totally ordered universe in this context. UR structures are also called "strongly history independent" structures in the literature. We introduce a two-layer data structure called (α,ε)-Randomized Block Search Tree (RBST) that is uniquely represented and suitable for external memory (EM). Though RBSTs naturally generalize the well-known binary Treaps, several new ideas are needed to analyze the expected search, update, and storage efficiency in terms of block-reads, block-writes, and blocks stored. We prove that searches have O(ε^{-1} + log_α n) block-reads, that dynamic updates perform O(ε^{-1} + log_α(n)/α) block-writes and O(ε^{-2}+(1+(ε^{-1}+log n)/α)log_α n) block-reads, and that (α, ε)-RBSTs have an asymptotic load-factor of at least (1-ε) for every ε ∈ (0,1/2]. Thus (α, ε)-RBSTs improve on the known, uniquely represented B-Treap [Golovin; ICALP'09]. Compared with non-UR structures, the RBST is also, to the best of our knowledge, the first external memory structure that is storage-efficient and has a non-amortized, write-efficient update bound.
Cite as

Roodabeh Safavi and Martin P. Seybold. B-Treaps Revised: Write Efficient Randomized Block Search Trees with High Load. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 47:1-47:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{safavi_et_al:LIPIcs.WADS.2025.47,
  author =	{Safavi, Roodabeh and Seybold, Martin P.},
  title =	{{B-Treaps Revised: Write Efficient Randomized Block Search Trees with High Load}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{47:1--47:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.47},
  URN =		{urn:nbn:de:0030-drops-242786},
  doi =		{10.4230/LIPIcs.WADS.2025.47},
  annote =	{Keywords: Unique Representation, Randomization, Top-Down Analysis, Block Search Tree, Write-Efficiency, Storage-Efficiency}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.54
The Fréchet Distance Unleashed: Approximating a Dog with a Frog

Authors: Sariel Har-Peled, Benjamin Raichel, and Eliot W. Robson

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

Abstract
We show that a variant of the continuous Fréchet distance between polygonal curves can be computed using essentially the same algorithm used to solve the discrete version. The new variant is not necessarily monotone, but this shortcoming can be easily handled via refinement. Combined with a Dijkstra/Prim type algorithm, this leads to a realization of the Fréchet distance (i.e., a morphing) that is locally optimal (aka locally correct), that is both easy to compute, and in practice, takes near linear time on many inputs. The new morphing has the property that the leash is always as short as possible. These matchings/morphings are more natural, and are better than the ones computed by standard algorithms - in particular, they handle noise more graciously. This should make the Fréchet distance more useful for real world applications. We implemented the new algorithm, and various strategies to obtain fast practical performance. We performed extensive experiments with our new algorithm, and released publicly available (and easily installable and usable) Julia and Python packages. In particular, the Julia implementation, for computing the regular Fréchet distance, seems to be {significantly faster} than other currently available implementations. See Table 2.2. Our algorithms can be used to compute the almost-exact Fréchet distance between polygonal curves. Implementations and numerous examples are available here: https://frechet.xyz.
Cite as

Sariel Har-Peled, Benjamin Raichel, and Eliot W. Robson. The Fréchet Distance Unleashed: Approximating a Dog with a Frog. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 54:1-54:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{harpeled_et_al:LIPIcs.SoCG.2025.54,
  author =	{Har-Peled, Sariel and Raichel, Benjamin and Robson, Eliot W.},
  title =	{{The Fr\'{e}chet Distance Unleashed: Approximating a Dog with a Frog}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{54:1--54:13},
  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.2025.54},
  URN =		{urn:nbn:de:0030-drops-232066},
  doi =		{10.4230/LIPIcs.SoCG.2025.54},
  annote =	{Keywords: Curve similarity, Fr\'{e}chet distance}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.18
A Simple Dynamization of Trapezoidal Point Location in Planar Subdivisions

Authors: Milutin Brankovic, Nikola Grujic, André van Renssen, and Martin P. Seybold

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
We study how to dynamize the Trapezoidal Search Tree (TST) - a well known randomized point location structure for planar subdivisions of kinetic line segments. Our approach naturally extends incremental leaf-level insertions to recursive methods and allows adaptation for the online setting. The dynamization carries over to the Trapezoidal Search DAG (TSD), which has linear size and logarithmic point location costs with high probability. On a set S of non-crossing segments, each TST update performs expected 𝒪(log²|S|) operations and each TSD update performs expected 𝒪(log |S|) operations. We demonstrate the practicality of our method with an open-source implementation, based on the Computational Geometry Algorithms Library, and experiments on the update performance.
Cite as

Milutin Brankovic, Nikola Grujic, André van Renssen, and Martin P. Seybold. A Simple Dynamization of Trapezoidal Point Location in Planar Subdivisions. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{brankovic_et_al:LIPIcs.ICALP.2020.18,
  author =	{Brankovic, Milutin and Grujic, Nikola and van Renssen, Andr\'{e} and Seybold, Martin P.},
  title =	{{A Simple Dynamization of Trapezoidal Point Location in Planar Subdivisions}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{18:1--18:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.18},
  URN =		{urn:nbn:de:0030-drops-124253},
  doi =		{10.4230/LIPIcs.ICALP.2020.18},
  annote =	{Keywords: Dynamization, Trapezoidal Search Tree, Trapezoidal Search DAG, Backward Analysis, Point Location, Planar Subdivision, Treap, Order-maintenance}
}
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