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Documents authored by Virk, Ziga

Found 2 Possible Name Variants:

Virk, Ziga

Document
DOI: 10.4230/LIPIcs.SoCG.2026.3
Lower Bounding the Gromov-Hausdorff Distance in Metric Graphs

Authors: Henry Adams, Sushovan Majhi, Fedor Manin, Žiga Virk, and Nicolò Zava

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
Let G be a finite, connected metric graph and let X be a subset of G. If X is sufficiently dense in G, we show that the Gromov-Hausdorff distance matches the Hausdorff distance, namely d_GH(G,X) = d_H(G,X). When the metric graph is the circle G = S¹ with circumference 2π, a recent study established the equality d_GH(S¹,X) = d_H(S¹,X) whenever d_GH(S¹,X) < π/6. Our results relax this hypothesis to d_GH(S¹,X) < π/3, and furthermore, we show that the constant π/3 is the best possible. We lower bound the Gromov-Hausdorff distance d_GH(G,X) by the Hausdorff distance d_H(G,X) via a simple topological obstruction: the existence of a possibly discontinuous function f: G → X with too small distortion contradicts the connectedness of G.
Cite as

Henry Adams, Sushovan Majhi, Fedor Manin, Žiga Virk, and Nicolò Zava. Lower Bounding the Gromov-Hausdorff Distance in Metric Graphs. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{adams_et_al:LIPIcs.SoCG.2026.3,
  author =	{Adams, Henry and Majhi, Sushovan and Manin, Fedor and Virk, \v{Z}iga and Zava, Nicol\`{o}},
  title =	{{Lower Bounding the Gromov-Hausdorff Distance in Metric Graphs}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{3:1--3:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.3},
  URN =		{urn:nbn:de:0030-drops-258099},
  doi =		{10.4230/LIPIcs.SoCG.2026.3},
  annote =	{Keywords: Gromov-Hausdorff distance, distortion, connectedness, Borsuk-Ulam theorem}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2019.31
Topological Data Analysis in Information Space

Authors: Herbert Edelsbrunner, Žiga Virk, and Hubert Wagner

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

Abstract
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a discrete probability distribution as a point in the standard simplex of the appropriate dimension, we can understand collections of such objects in geometric and topological terms. Importantly, instead of using the standard Euclidean distance, we look into dissimilarity measures with information-theoretic justification, and we develop the theory needed for applying topological data analysis in this setting. In doing so, we emphasize constructions that enable the usage of existing computational topology software in this context.
Cite as

Herbert Edelsbrunner, Žiga Virk, and Hubert Wagner. Topological Data Analysis in Information Space. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{edelsbrunner_et_al:LIPIcs.SoCG.2019.31,
  author =	{Edelsbrunner, Herbert and Virk, \v{Z}iga and Wagner, Hubert},
  title =	{{Topological Data Analysis in Information Space}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{31:1--31:14},
  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.2019.31},
  URN =		{urn:nbn:de:0030-drops-104357},
  doi =		{10.4230/LIPIcs.SoCG.2019.31},
  annote =	{Keywords: Computational topology, persistent homology, information theory, entropy}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2018.35
Smallest Enclosing Spheres and Chernoff Points in BregmanGeometry

Authors: Herbert Edelsbrunner, Ziga Virk, and Hubert Wagner

Published in: LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018)

Abstract
Smallest enclosing spheres of finite point sets are central to methods in topological data analysis. Focusing on Bregman divergences to measure dissimilarity, we prove bounds on the location of the center of a smallest enclosing sphere. These bounds depend on the range of radii for which Bregman balls are convex.
Cite as

Herbert Edelsbrunner, Ziga Virk, and Hubert Wagner. Smallest Enclosing Spheres and Chernoff Points in BregmanGeometry. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 35:1-35:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{edelsbrunner_et_al:LIPIcs.SoCG.2018.35,
  author =	{Edelsbrunner, Herbert and Virk, Ziga and Wagner, Hubert},
  title =	{{Smallest Enclosing Spheres and Chernoff Points in BregmanGeometry}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{35:1--35:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Speckmann, Bettina and T\'{o}th, Csaba D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.35},
  URN =		{urn:nbn:de:0030-drops-87487},
  doi =		{10.4230/LIPIcs.SoCG.2018.35},
  annote =	{Keywords: Bregman divergence, smallest enclosing spheres, Chernoff points, convexity, barycenter polytopes}
}

Virk, Žiga

Document
DOI: 10.4230/LIPIcs.SoCG.2026.3
Lower Bounding the Gromov-Hausdorff Distance in Metric Graphs

Authors: Henry Adams, Sushovan Majhi, Fedor Manin, Žiga Virk, and Nicolò Zava

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
Let G be a finite, connected metric graph and let X be a subset of G. If X is sufficiently dense in G, we show that the Gromov-Hausdorff distance matches the Hausdorff distance, namely d_GH(G,X) = d_H(G,X). When the metric graph is the circle G = S¹ with circumference 2π, a recent study established the equality d_GH(S¹,X) = d_H(S¹,X) whenever d_GH(S¹,X) < π/6. Our results relax this hypothesis to d_GH(S¹,X) < π/3, and furthermore, we show that the constant π/3 is the best possible. We lower bound the Gromov-Hausdorff distance d_GH(G,X) by the Hausdorff distance d_H(G,X) via a simple topological obstruction: the existence of a possibly discontinuous function f: G → X with too small distortion contradicts the connectedness of G.
Cite as

Henry Adams, Sushovan Majhi, Fedor Manin, Žiga Virk, and Nicolò Zava. Lower Bounding the Gromov-Hausdorff Distance in Metric Graphs. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{adams_et_al:LIPIcs.SoCG.2026.3,
  author =	{Adams, Henry and Majhi, Sushovan and Manin, Fedor and Virk, \v{Z}iga and Zava, Nicol\`{o}},
  title =	{{Lower Bounding the Gromov-Hausdorff Distance in Metric Graphs}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{3:1--3:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.3},
  URN =		{urn:nbn:de:0030-drops-258099},
  doi =		{10.4230/LIPIcs.SoCG.2026.3},
  annote =	{Keywords: Gromov-Hausdorff distance, distortion, connectedness, Borsuk-Ulam theorem}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2019.31
Topological Data Analysis in Information Space

Authors: Herbert Edelsbrunner, Žiga Virk, and Hubert Wagner

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

Abstract
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a discrete probability distribution as a point in the standard simplex of the appropriate dimension, we can understand collections of such objects in geometric and topological terms. Importantly, instead of using the standard Euclidean distance, we look into dissimilarity measures with information-theoretic justification, and we develop the theory needed for applying topological data analysis in this setting. In doing so, we emphasize constructions that enable the usage of existing computational topology software in this context.
Cite as

Herbert Edelsbrunner, Žiga Virk, and Hubert Wagner. Topological Data Analysis in Information Space. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{edelsbrunner_et_al:LIPIcs.SoCG.2019.31,
  author =	{Edelsbrunner, Herbert and Virk, \v{Z}iga and Wagner, Hubert},
  title =	{{Topological Data Analysis in Information Space}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{31:1--31:14},
  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.2019.31},
  URN =		{urn:nbn:de:0030-drops-104357},
  doi =		{10.4230/LIPIcs.SoCG.2019.31},
  annote =	{Keywords: Computational topology, persistent homology, information theory, entropy}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2018.35
Smallest Enclosing Spheres and Chernoff Points in BregmanGeometry

Authors: Herbert Edelsbrunner, Ziga Virk, and Hubert Wagner

Published in: LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018)

Abstract
Smallest enclosing spheres of finite point sets are central to methods in topological data analysis. Focusing on Bregman divergences to measure dissimilarity, we prove bounds on the location of the center of a smallest enclosing sphere. These bounds depend on the range of radii for which Bregman balls are convex.
Cite as

Herbert Edelsbrunner, Ziga Virk, and Hubert Wagner. Smallest Enclosing Spheres and Chernoff Points in BregmanGeometry. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 35:1-35:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{edelsbrunner_et_al:LIPIcs.SoCG.2018.35,
  author =	{Edelsbrunner, Herbert and Virk, Ziga and Wagner, Hubert},
  title =	{{Smallest Enclosing Spheres and Chernoff Points in BregmanGeometry}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{35:1--35:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Speckmann, Bettina and T\'{o}th, Csaba D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.35},
  URN =		{urn:nbn:de:0030-drops-87487},
  doi =		{10.4230/LIPIcs.SoCG.2018.35},
  annote =	{Keywords: Bregman divergence, smallest enclosing spheres, Chernoff points, convexity, barycenter polytopes}
}
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