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An Experimental Study on the Ply Number of Straight-Line Drawings

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WALCOM: Algorithms and Computation (WALCOM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10167))

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Abstract

The ply number of a drawing is a new criterion of interest for graph drawing. Informally, the ply number of a straight-line drawing of a graph is defined as the maximum number of overlapping disks, where each disk is associated with a vertex and has a radius that is half the length of the longest edge incident to that vertex. This paper reports the results of an extensive experimental study that attempts to estimate correlations between the ply numbers and other aesthetic quality metrics for a graph layout, such as stress, edge-length uniformity, and edge crossings. We also investigate the performances of several graph drawing algorithms in terms of ply number, and provides new insights on the theoretical gap between lower and upper bounds on the ply number of k-ary trees.

Research supported in part by the MIUR project AMANDA “Algorithmics for MAssive and Networked DAta”, prot. 2012C4E3KT_001. Work on this problem began at the NII Shonan Meeting Big Graph Drawing: Metrics and Methods, Jan. 12–15, 2015. We thank M. Kaufmann and his staff in the University of Tübingen for sharing their code to compute ply number. We also thank A. Wolff and F. Montecchiani for many useful discussions.

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Authors and Affiliations

  1. Università degli Studi di Perugia, Perugia, Italy

    Felice De Luca, Emilio Di Giacomo, Walter Didimo & Giuseppe Liotta

  2. University of Arizona, Tucson, USA

    Stephen Kobourov

Authors
  1. Felice De Luca
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  2. Emilio Di Giacomo
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  3. Walter Didimo
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  4. Stephen Kobourov
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  5. Giuseppe Liotta
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Correspondence to Felice De Luca .

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Editors and Affiliations

  1. Universiti Teknologi Brunei, Bandar Seri Begawan, Brunei Darussalam

    Sheung-Hung Poon

  2. Bangladesh University of Engineering and Technology, Dhaka, Bangladesh

    Md. Saidur Rahman

  3. National Taiwan University, Taipei, Taiwan

    Hsu-Chun Yen

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De Luca, F., Di Giacomo, E., Didimo, W., Kobourov, S., Liotta, G. (2017). An Experimental Study on the Ply Number of Straight-Line Drawings. In: Poon, SH., Rahman, M., Yen, HC. (eds) WALCOM: Algorithms and Computation. WALCOM 2017. Lecture Notes in Computer Science(), vol 10167. Springer, Cham. https://doi.org/10.1007/978-3-319-53925-6_11

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  • DOI: https://doi.org/10.1007/978-3-319-53925-6_11

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