SERIE B INFORMATIK Voronoi Diagrams of Lines in Space Under Polyhedral Convex Distance Functions
نویسندگان
چکیده
The combinatorial complexity of the Voronoi diagram of n lines in three dimensions under a convex distance function induced by a polytope with a constant number of edges is shown to be O n n log n where is a slowly growing inverse of the Ackermann function There are arrangements of n lines where this complexity can be as large as n n Work by Paul Chew and Klara Kedem has been supported by AFOSR Grant AFOSR Work by Paul Chew has also been supported by ONR Grant N J and ARPA under ONR contract N K Work by Micha Sharir and Emo Welzl has been supported by the G I F the German Israeli Foundation for Scienti c Research and Development and by a Max Planck Research Award Work by Micha Sharir has also been supported by National Science Foundation Grant CCR and by grants from the U S Israeli Binational Science Foundation and the Israel Science Fund administered by the Israeli Academy of Sciences Work by Emo Welzl has also been supported by the EC Basic Research Action Project ALCOM II Department of Computer Science Cornell University Ithaca NY USA chew cs cornell edu Department of Mathematics and Computer Science Ben Gurion University Beer Sheva Israel klara ivory bgu ac il School of Mathematical Sciences Tel Aviv University and Courant Institute of Mathematical Sciences New York University sharir math tau ac il School of Mathematical Sciences Tel Aviv University Institut f ur Informatik Freie Universit at Berlin Takustr D Berlin Germany emo inf fu berlin de
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