[{"publisher":"Springer Nature","publication":"Graph Drawing and Network Visualization","publication_status":"published","abstract":[{"text":"The straight skeleton of a polygon is the geometric graph obtained by tracing the vertices during a mitered offsetting process. It is known that the straight skeleton of a simple polygon is a tree, and one can naturally derive directions on the edges of the tree from the propagation of the shrinking process. In this paper, we ask the reverse question: Given a tree with directed edges, can it be the straight skeleton of a polygon? And if so, can we find a suitable simple polygon? We answer these questions for all directed trees where the order of edges around each node is fixed.","lang":"eng"}],"doi":"10.1007/978-3-319-27261-0_28","status":"public","date_created":"2018-12-11T11:52:54Z","conference":{"name":"GD: International Symposium on Graph Drawing","start_date":"2015-09-24","end_date":"2015-09-26","location":"Los Angeles, CA, United States"},"alternative_title":["LNCS"],"page":"335 - 347","scopus_import":"1","intvolume":"      9411","quality_controlled":"1","volume":9411,"title":"Representing directed trees as straight skeletons","author":[{"last_name":"Aichholzer","first_name":"Oswin","full_name":"Aichholzer, Oswin"},{"full_name":"Biedl, Therese","last_name":"Biedl","first_name":"Therese"},{"first_name":"Thomas","last_name":"Hackl","full_name":"Hackl, Thomas"},{"first_name":"Martin","last_name":"Held","full_name":"Held, Martin"},{"id":"4700A070-F248-11E8-B48F-1D18A9856A87","full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","first_name":"Stefan","last_name":"Huber"},{"full_name":"Palfrader, Peter","last_name":"Palfrader","first_name":"Peter"},{"full_name":"Vogtenhuber, Birgit","last_name":"Vogtenhuber","first_name":"Birgit"}],"day":"27","date_published":"2015-11-27T00:00:00Z","type":"book_chapter","article_processing_charge":"No","main_file_link":[{"url":"http://arxiv.org/abs/1508.01076","open_access":"1"}],"citation":{"ista":"Aichholzer O, Biedl T, Hackl T, Held M, Huber S, Palfrader P, Vogtenhuber B. 2015.Representing directed trees as straight skeletons. In: Graph Drawing and Network Visualization. LNCS, vol. 9411, 335–347.","mla":"Aichholzer, Oswin, et al. “Representing Directed Trees as Straight Skeletons.” <i>Graph Drawing and Network Visualization</i>, vol. 9411, Springer Nature, 2015, pp. 335–47, doi:<a href=\"https://doi.org/10.1007/978-3-319-27261-0_28\">10.1007/978-3-319-27261-0_28</a>.","ama":"Aichholzer O, Biedl T, Hackl T, et al. Representing directed trees as straight skeletons. In: <i>Graph Drawing and Network Visualization</i>. Vol 9411. Springer Nature; 2015:335-347. doi:<a href=\"https://doi.org/10.1007/978-3-319-27261-0_28\">10.1007/978-3-319-27261-0_28</a>","short":"O. Aichholzer, T. Biedl, T. Hackl, M. Held, S. Huber, P. Palfrader, B. Vogtenhuber, in:, Graph Drawing and Network Visualization, Springer Nature, 2015, pp. 335–347.","chicago":"Aichholzer, Oswin, Therese Biedl, Thomas Hackl, Martin Held, Stefan Huber, Peter Palfrader, and Birgit Vogtenhuber. “Representing Directed Trees as Straight Skeletons.” In <i>Graph Drawing and Network Visualization</i>, 9411:335–47. Springer Nature, 2015. <a href=\"https://doi.org/10.1007/978-3-319-27261-0_28\">https://doi.org/10.1007/978-3-319-27261-0_28</a>.","apa":"Aichholzer, O., Biedl, T., Hackl, T., Held, M., Huber, S., Palfrader, P., &#38; Vogtenhuber, B. (2015). Representing directed trees as straight skeletons. In <i>Graph Drawing and Network Visualization</i> (Vol. 9411, pp. 335–347). Los Angeles, CA, United States: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-27261-0_28\">https://doi.org/10.1007/978-3-319-27261-0_28</a>","ieee":"O. Aichholzer <i>et al.</i>, “Representing directed trees as straight skeletons,” in <i>Graph Drawing and Network Visualization</i>, vol. 9411, Springer Nature, 2015, pp. 335–347."},"month":"11","oa":1,"publication_identifier":{"eisbn":["978-3-319-27261-0"],"isbn":["978-3-319-27260-3"]},"oa_version":"Preprint","date_updated":"2022-01-28T09:10:37Z","publist_id":"5581","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","department":[{"_id":"HeEd"}],"language":[{"iso":"eng"}],"_id":"1590","year":"2015"},{"intvolume":"      9411","scopus_import":"1","page":"373 - 379","author":[{"last_name":"Fulek","first_name":"Radoslav","orcid":"0000-0001-8485-1774","full_name":"Fulek, Radoslav","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Radoičić, Radoš","last_name":"Radoičić","first_name":"Radoš"}],"day":"27","volume":9411,"quality_controlled":"1","file":[{"file_id":"5258","creator":"system","file_size":312992,"file_name":"IST-2016-595-v1+1_VerticalVisibilityGDRevision.pdf","date_created":"2018-12-12T10:17:06Z","content_type":"application/pdf","checksum":"eec04f86c5921d04f025d5791db9b965","date_updated":"2020-07-14T12:45:04Z","relation":"main_file","access_level":"open_access"}],"title":"Vertical visibility among parallel polygons in three dimensions","ec_funded":1,"publication":"Graph Drawing and Network Visualization","publication_status":"published","publisher":"Springer Nature","file_date_updated":"2020-07-14T12:45:04Z","abstract":[{"lang":"eng","text":"Let C={C1,...,Cn} denote a collection of translates of a regular convex k-gon in the plane with the stacking order. The collection C forms a visibility clique if for everyi &lt; j the intersection Ci and (Ci ∩ Cj)\\⋃i&lt;l&lt;jCl =∅.elements that are stacked between them, i.e., We show that if C forms a visibility clique its size is bounded from above by O(k4) thereby improving the upper bound of 22k from the aforementioned paper. We also obtain an upper bound of 22(k/2)+2 on the size of a visibility clique for homothetes of a convex (not necessarily regular) k-gon."}],"doi":"10.1007/978-3-319-27261-0_31","date_created":"2018-12-11T11:52:56Z","status":"public","pubrep_id":"595","alternative_title":["LNCS"],"conference":{"location":"Los Angeles, CA, United States","name":"GD: Graph Drawing and Network Visualization","start_date":"2015-09-24","end_date":"2015-09-26"},"has_accepted_license":"1","date_updated":"2022-01-28T09:20:50Z","publist_id":"5575","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","department":[{"_id":"UlWa"}],"project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"year":"2015","language":[{"iso":"eng"}],"_id":"1596","type":"book_chapter","date_published":"2015-11-27T00:00:00Z","citation":{"ieee":"R. Fulek and R. Radoičić, “Vertical visibility among parallel polygons in three dimensions,” in <i>Graph Drawing and Network Visualization</i>, vol. 9411, Springer Nature, 2015, pp. 373–379.","chicago":"Fulek, Radoslav, and Radoš Radoičić. “Vertical Visibility among Parallel Polygons in Three Dimensions.” In <i>Graph Drawing and Network Visualization</i>, 9411:373–79. Springer Nature, 2015. <a href=\"https://doi.org/10.1007/978-3-319-27261-0_31\">https://doi.org/10.1007/978-3-319-27261-0_31</a>.","apa":"Fulek, R., &#38; Radoičić, R. (2015). Vertical visibility among parallel polygons in three dimensions. In <i>Graph Drawing and Network Visualization</i> (Vol. 9411, pp. 373–379). Los Angeles, CA, United States: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-27261-0_31\">https://doi.org/10.1007/978-3-319-27261-0_31</a>","ama":"Fulek R, Radoičić R. Vertical visibility among parallel polygons in three dimensions. In: <i>Graph Drawing and Network Visualization</i>. Vol 9411. Springer Nature; 2015:373-379. doi:<a href=\"https://doi.org/10.1007/978-3-319-27261-0_31\">10.1007/978-3-319-27261-0_31</a>","short":"R. Fulek, R. Radoičić, in:, Graph Drawing and Network Visualization, Springer Nature, 2015, pp. 373–379.","ista":"Fulek R, Radoičić R. 2015.Vertical visibility among parallel polygons in three dimensions. In: Graph Drawing and Network Visualization. LNCS, vol. 9411, 373–379.","mla":"Fulek, Radoslav, and Radoš Radoičić. “Vertical Visibility among Parallel Polygons in Three Dimensions.” <i>Graph Drawing and Network Visualization</i>, vol. 9411, Springer Nature, 2015, pp. 373–79, doi:<a href=\"https://doi.org/10.1007/978-3-319-27261-0_31\">10.1007/978-3-319-27261-0_31</a>."},"article_processing_charge":"No","month":"11","oa":1,"oa_version":"Submitted Version","ddc":["510"],"publication_identifier":{"isbn":["978-3-319-27260-3"]}}]