{"abstract":[{"text":"This note proves that the maximum number of faces (of any dimension) of the upper envelope of a set ofn possibly intersectingd-simplices ind+1 dimensions is (n d (n)). This is an extension of a result of Pach and Sharir [PS] who prove the same bound for the number ofd-dimensional faces of the upper envelope.","lang":"eng"}],"publisher":"Springer","publist_id":"2034","issue":"4","language":[{"iso":"eng"}],"article_processing_charge":"No","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","scopus_import":"1","doi":"10.1007/BF02187734","citation":{"apa":"Edelsbrunner, H. (1989). The upper envelope of piecewise linear functions: Tight bounds on the number of faces . <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/BF02187734\">https://doi.org/10.1007/BF02187734</a>","short":"H. Edelsbrunner, Discrete &#38; Computational Geometry 4 (1989) 337–343.","ista":"Edelsbrunner H. 1989. The upper envelope of piecewise linear functions: Tight bounds on the number of faces . Discrete &#38; Computational Geometry. 4(4), 337–343.","mla":"Edelsbrunner, Herbert. “The Upper Envelope of Piecewise Linear Functions: Tight Bounds on the Number of Faces .” <i>Discrete &#38; Computational Geometry</i>, vol. 4, no. 4, Springer, 1989, pp. 337–43, doi:<a href=\"https://doi.org/10.1007/BF02187734\">10.1007/BF02187734</a>.","chicago":"Edelsbrunner, Herbert. “The Upper Envelope of Piecewise Linear Functions: Tight Bounds on the Number of Faces .” <i>Discrete &#38; Computational Geometry</i>. Springer, 1989. <a href=\"https://doi.org/10.1007/BF02187734\">https://doi.org/10.1007/BF02187734</a>.","ieee":"H. Edelsbrunner, “The upper envelope of piecewise linear functions: Tight bounds on the number of faces ,” <i>Discrete &#38; Computational Geometry</i>, vol. 4, no. 4. Springer, pp. 337–343, 1989.","ama":"Edelsbrunner H. The upper envelope of piecewise linear functions: Tight bounds on the number of faces . <i>Discrete &#38; Computational Geometry</i>. 1989;4(4):337-343. doi:<a href=\"https://doi.org/10.1007/BF02187734\">10.1007/BF02187734</a>"},"status":"public","day":"01","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"date_published":"1989-11-01T00:00:00Z","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02187734","open_access":"1"}],"quality_controlled":"1","publication":"Discrete & Computational Geometry","extern":"1","intvolume":"         4","acknowledgement":"This work was supported by Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and by the National Science Foundation under Grant CCR-8714565. Research on the presented result was partially carried out while the author worked for the IBM T. J. Watson Research Center at Yorktown Height, New York, USA. \r\n","article_type":"original","oa":1,"oa_version":"Published Version","publication_status":"published","type":"journal_article","year":"1989","author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"title":"The upper envelope of piecewise linear functions: Tight bounds on the number of faces ","_id":"4086","date_created":"2018-12-11T12:06:51Z","volume":4,"page":"337 - 343","month":"11","date_updated":"2022-02-10T11:08:12Z"}