@inproceedings{ec76cdefcffe4eb4bbd5d27e99ff7681,

title = "Computing depth orders and related problems",

abstract = "Let K: be a set of n non-intersecting objects in 3-space. A depth order of K, if exists, is a linear order < of the objects in K such that if K, L ε K: and K lies vertically below L then K < L. We present a new technique for computing depth orders, and apply it to several special classes of objects. Our results include: (i) If K is a set of n triangles whose xy-projections are all {\textquoteleft}fat{\textquoteright}, then a depth order for K: can be computed in time O(n log6 n). (ii) If K: is a set of n convex and simply-shaped objects whose xy-projections are all {\textquoteleft}fat{\textquoteright} and their sizes axe within a constant ratio from one another, then a depth order for K: can be computed in time O(nλs1/2 12 (n)log4 n), where s is the maximum number of intersections between the xy-projections of the boundaries of any pair of objects in/C.",

author = "Agarwal, {Pankaj K.} and Katz, {Matthew J.} and Micha Sharir",

note = "Publisher Copyright: {\textcopyright} 1994, Springer Verlag. All rights reserved.; 4th Scandinavian Workshop on Algorithm Theory, SWAT 1994 ; Conference date: 06-07-1994 Through 08-07-1994",

year = "1994",

month = jan,

day = "1",

doi = "10.1007/3-540-58218-5_1",

language = "English",

isbn = "9783540582182",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "1--12",

editor = "Schmidt, {Erik M.} and Sven Skyum",

booktitle = "Algorithm Theory – SWAT 1994 - 4th Scandinavian Workshop on Algorithm Theory, Proceedings",

address = "Germany",

}