[{"conference":{"name":"New Results and New Trends in Computer Science "},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publist_id":"2068","date_created":"2018-12-11T12:06:40Z","date_published":"1991-11-13T00:00:00Z","day":"13","intvolume":"       555","doi":"10.1007/BFb0038185","type":"conference","status":"public","volume":555,"date_updated":"2022-02-28T15:13:37Z","publication_status":"published","main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/BFb0038185"}],"page":"108 - 123","year":"1991","author":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"first_name":"Raimund","full_name":"Seidel, Raimund","last_name":"Seidel"},{"full_name":"Sharir, Micha","first_name":"Micha","last_name":"Sharir"}],"citation":{"chicago":"Edelsbrunner, Herbert, Raimund Seidel, and Micha Sharir. “On the Zone Theorem for Hyperplane Arrangements,” 555:108–23. Springer, 1991. <a href=\"https://doi.org/10.1007/BFb0038185\">https://doi.org/10.1007/BFb0038185</a>.","mla":"Edelsbrunner, Herbert, et al. <i>On the Zone Theorem for Hyperplane Arrangements</i>. Vol. 555, Springer, 1991, pp. 108–23, doi:<a href=\"https://doi.org/10.1007/BFb0038185\">10.1007/BFb0038185</a>.","apa":"Edelsbrunner, H., Seidel, R., &#38; Sharir, M. (1991). On the zone theorem for hyperplane arrangements (Vol. 555, pp. 108–123). Presented at the New Results and New Trends in Computer Science , Springer. <a href=\"https://doi.org/10.1007/BFb0038185\">https://doi.org/10.1007/BFb0038185</a>","ieee":"H. Edelsbrunner, R. Seidel, and M. Sharir, “On the zone theorem for hyperplane arrangements,” presented at the New Results and New Trends in Computer Science , 1991, vol. 555, pp. 108–123.","ista":"Edelsbrunner H, Seidel R, Sharir M. 1991. On the zone theorem for hyperplane arrangements. New Results and New Trends in Computer Science , LNCS, vol. 555, 108–123.","short":"H. Edelsbrunner, R. Seidel, M. Sharir, in:, Springer, 1991, pp. 108–123.","ama":"Edelsbrunner H, Seidel R, Sharir M. On the zone theorem for hyperplane arrangements. In: Vol 555. Springer; 1991:108-123. doi:<a href=\"https://doi.org/10.1007/BFb0038185\">10.1007/BFb0038185</a>"},"abstract":[{"text":"The zone theorem for an arrangement of n hyperplanes in d-dimensional real space says that the total number of faces bounding the cells intersected by another hyperplane is O(n d–1). This result is the basis of a time-optimal incremental algorithm that constructs a hyperplane arrangement and has a host of other algorithmic and combinatorial applications. Unfortunately, the original proof of the zone theorem, for d ge 3, turned out to contain a serious and irreparable error. This paper presents a new proof of the theorem. Our proof is based on an inductive argument, which also applies in the case of pseudo-hyperplane arrangements. We also briefly discuss the fallacies of the old proof along with some ways of partially saving that approach.","lang":"eng"}],"quality_controlled":"1","article_processing_charge":"No","publisher":"Springer","oa_version":"None","_id":"4054","extern":"1","alternative_title":["LNCS"],"language":[{"iso":"eng"}],"acknowledgement":"Research of Herbert Edelsbrunner was supported by the National Science Foundation under grant CCR-89-21421. Raimund Seidel acknowledges support by an NSF Presidential Young Investigator Grant CCR-90-58440. Micha Sharir has been supported by ONR Grant N00014-90-J-1284, by NSF Grant CCR-89-01484, and by grants from the U.S.-Israeli Binational Science Foundation, the German-Israeli Foundation for Scientific Research and Development, and the Fund for Basic Research of the Israeli Academy of Sciences.","month":"11","title":"On the zone theorem for hyperplane arrangements"}]