@article{821f218384c14a52810ea391d5e4771d,
title = "An experimental study on the ply number of straight-line drawings",
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 number and other aesthetic quality metrics for a graph layout, such as stress, edge-length uniformity, and edge crossings. We also investigate the performance of several graph drawing algorithms in terms of ply number, and provide new insights into the theoretical gap between lower and upper bounds on the ply number of k-ary trees.",
author = "{De Luca}, Felice and {Di Giacomo}, Emilio and Walter Didimo and Stephen Kobourov and Giuseppe Liotta",
note = "Funding Information: June 2018 August 2018 Final: Published: August 2018 January 2019 Communicated by: M.S. Rahman, H.-C. Yen and S.-H. Poon 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 T{\"u}bingen for sharing their code to compute ply number. We also thank A. Wolff and F. Montecchiani for many useful discussions. This work is supported in part by NSF grants CCF-1740858, CCF-1712119, DMS-1839274, and DMS-1839307 and by the project “Algoritmi e sistemi di analisi visuale di reti complesse e di grandi dimensioni” - Ricerca di Base 2018, Dipartimento di Ingegneria dell{\textquoteright}Universit{\`a} degli Studi di Perugia. E-mail addresses: felicedeluca@email.arizona.edu (Felice De Luca) emilio.digiacomo@unipg.it (Emilio Di Giacomo) walter.didimo@unipg.it (Walter Didimo) kobourov@cs.arizona.edu (Stephen Kobourov) giuseppe.liotta@unipg.it (Giuseppe Liotta) Funding Information: We also thank A. Wolff and F. Montecchiani for many useful discussions. This work is supported in part by NSF grants CCF-1740858, CCF-1712119, DMS-1839274, and DMS-1839307 and by the project \Algoritmi e sistemi di analisi visuale di reti complesse e di grandi dimensioni? - Ricerca di Base 2018, Dipartimento di Ingegneria dell?Universit? degli Studi di Perugia. Publisher Copyright: {\textcopyright} 2019, Brown University. All rights reserved.",
year = "2019",
doi = "10.7155/JGAA.00484",
language = "English (US)",
volume = "23",
pages = "71--91",
journal = "Journal of Graph Algorithms and Applications",
issn = "1526-1719",
publisher = "Brown University",
number = "1",
}