@inproceedings{63b36ca7b4ca46c9a1261cc21db4068d,

title = "Combinatorial complexity of signed discs",

abstract = "Let C+ and C− be two collections of topological discs of arbitrary radii. The collection of discs is {\textquoteleft}topological{\textquoteright} in the sense that their boundaries are Jordan curves and each pair of Jordan curves intersect at most twice. We prove that the region ∪C+−∪C− has combinatorial complexity at most 10n-30 where p=|C+|, q=|C−| and n=p + q ≥ 5. Moreover, this bound is achievable. We also show bounds that are stated as functions of p and q. These are less precise.",

author = "Souvaine, {Diane L.} and Yap, {Chee Keng}",

note = "Funding Information: *This work originated at the ParallelA lgorithms and ComputationalG eometryWorkshop (1991)a t McGin University'Bs ellairsR esearcCh entera ndw ass upporteidn part by NSF grants~ DCR-84-01898, #CCR-87-0345~8,C CR-88-0354a9n d~ CCR-91-04732. IDept. of ComputeSr cienceR, utgersU niversityN,e wB runswickN, ewJ ersey0 8903d, lsOcs.rutgers.edu. IDept. of ComputeSr cienceN, ewY ork UniversityN,e wY ork,N ewY ork 10012y, ap@cs.nyu.edu.; 3rd Workshop on Algorithms and Data Structures, WADS 1993 ; Conference date: 11-08-1993 Through 13-08-1993",

year = "1993",

doi = "10.1007/3-540-57155-8_281",

language = "English (US)",

isbn = "9783540571551",

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

publisher = "Springer Verlag",

pages = "577--588",

editor = "Frank Dehne and Jorg-Rudiger Sack and Nicola Santoro and Sue Whitesides",

booktitle = "Algorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings",

}