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DOI: 10.4230/LIPIcs.SEA.2020.25

Zipping Segment Trees

Authors: Lukas Barth and Dorothea Wagner

Published in: LIPIcs, Volume 160, 18th International Symposium on Experimental Algorithms (SEA 2020)

Abstract

Stabbing queries in sets of intervals are usually answered using segment trees. A dynamic variant of segment trees has been presented by van Kreveld and Overmars, which uses red-black trees to do rebalancing operations. This paper presents zipping segment trees - dynamic segment trees based on zip trees, which were recently introduced by Tarjan et al. To facilitate zipping segment trees, we show how to uphold certain segment tree properties during the operations of a zip tree. We present an in-depth experimental evaluation and comparison of dynamic segment trees based on red-black trees, weight-balanced trees and several variants of the novel zipping segment trees. Our results indicate that zipping segment trees perform better than rotation-based alternatives.

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Lukas Barth and Dorothea Wagner. Zipping Segment Trees. In 18th International Symposium on Experimental Algorithms (SEA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 160, pp. 25:1-25:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{barth_et_al:LIPIcs.SEA.2020.25,
  author =	{Barth, Lukas and Wagner, Dorothea},
  title =	{{Zipping Segment Trees}},
  booktitle =	{18th International Symposium on Experimental Algorithms (SEA 2020)},
  pages =	{25:1--25:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-148-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{160},
  editor =	{Faro, Simone and Cantone, Domenico},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2020.25},
  URN =		{urn:nbn:de:0030-drops-120990},
  doi =		{10.4230/LIPIcs.SEA.2020.25},
  annote =	{Keywords: Segment Trees, Dynamic Segment Trees, Zip Trees, Data Structures}
}

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DOI: 10.4230/LIPIcs.SoCG.2017.14

Towards a Topology-Shape-Metrics Framework for Ortho-Radial Drawings

Authors: Lukas Barth, Benjamin Niedermann, Ignaz Rutter, and Matthias Wolf

Published in: LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017)

Abstract

Ortho-Radial drawings are a generalization of orthogonal drawings to grids that are formed by concentric circles and straight-line spokes emanating from the circles' center. Such drawings have applications in schematic graph layouts, e.g., for metro maps and destination maps. A plane graph is a planar graph with a fixed planar embedding. We give a combinatorial characterization of the plane graphs that admit a planar ortho-radial drawing without bends. Previously, such a characterization was only known for paths, cycles, and theta graphs, and in the special case of rectangular drawings for cubic graphs, where the contour of each face is required to be a rectangle. The characterization is expressed in terms of an ortho-radial representation that, similar to Tamassia's orthogonal representations for orthogonal drawings describes such a drawing combinatorially in terms of angles around vertices and bends on the edges. In this sense our characterization can be seen as a first step towards generalizing the Topology-Shape-Metrics framework of Tamassia to ortho-radial drawings.

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Lukas Barth, Benjamin Niedermann, Ignaz Rutter, and Matthias Wolf. Towards a Topology-Shape-Metrics Framework for Ortho-Radial Drawings. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 14:1-14:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{barth_et_al:LIPIcs.SoCG.2017.14,
  author =	{Barth, Lukas and Niedermann, Benjamin and Rutter, Ignaz and Wolf, Matthias},
  title =	{{Towards a Topology-Shape-Metrics Framework for Ortho-Radial Drawings}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{14:1--14:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Aronov, Boris and Katz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.14},
  URN =		{urn:nbn:de:0030-drops-72234},
  doi =		{10.4230/LIPIcs.SoCG.2017.14},
  annote =	{Keywords: Graph Drawing, Ortho-Radial Drawings, Combinatorial Characterization, Bend Minimization, Topology-Shape-Metrics}
}

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Documents authored by Barth, Lukas

Zipping Segment Trees

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Towards a Topology-Shape-Metrics Framework for Ortho-Radial Drawings

Abstract

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