article{em-nsme-97 , author = "J. Edmonds and J.-F. Maurras" , title = "Note sur les $Q$-matrices d'Edmonds" , journal = "Recherche Op{\'e}rationnelle (RAIRO)" , volume = 31 , number = 2 , year = 1997 , pages = "203--209" } @inproceedings{g-ealcc-98 , author = "Bernd G{\"a}rtner" , title = "Exact Arithmetic at Low Cost: {A} Case Study in Linear Programming" , booktitle = "Proc. 9th ACM-SIAM Sympos. Discrete Algorithms" , nickname = "SODA '98" , year = 1998 , pages = "157--166" , update = "99.07 bibrelex, 98.07 mitchell" } @article{k-rprnmc-96 , author = "L. Khachiyan" , title = "Rounding of polytopes in the real number model of computation" , journal = "Math. Oper. Res." , volume = 21 , number = 2 , year = 1996 , pages = "307--320" } @misc{kmy-ccsasehhd-03 , author = "P. Kumar and J. S. B. Mitchell and E. A. Y{\i}ld{\i}r{\i}m" , title = "Computing core-sets and approximate smallest enclosing hyperspheres in high dimensions" , note = "To appear in the Proceedings of ALENEX'03." } @inproceedings{kjs-sstiissshdfs-97 , author = "R. Kurniawati and J. S. Jin and J. A. Shepherd", title = "The {SS$^+$}-tree: an improved index structure for similarity searches in a high-dimensional feature space", booktitle = "Proc. 5th Storage and Retrieval for Image and Video Databases {SPIE}", pages = "110--120", year = "1997", volume = "3022" } @article{m-ltalp-83 , author = "N. Megiddo" , title = "Linear-time algorithms for linear programming in {$R^{3}$} and related problems" , journal = "SIAM J. Comput." , volume = 12 , number = 4 , year = 1983 , pages = "759--776" , keywords = "design of algorithms, linear programming, three-dimensional, graph theory, prune-and-search, geometric transformat\ ions, points, lines, planes" , succeeds = "m-ltalp-82" , update = "01.04 icking" } @article{msw-sblp-96 , author = "J. Matou{\v s}ek and Micha Sharir and Emo Welzl" , title = "A subexponential bound for linear programming" , journal = "Algorithmica" , volume = 16 , year = 1996 , pages = "498--516" , update = "98.03 mitchell, 97.03 agarwal+smid" } @article{cm-ltdao-96 , author = "Bernard Chazelle and J. Matou{\v s}ek" , title = "On Linear-Time Deterministic Algorithms for Optimization Problems in Fixed Dimension" , journal = "J. Algorithms" , volume = 21 , year = 1996 , pages = "579--597" , update = "98.03 mitchell, 97.03 agarwal+smid, 96.09 agarwal, 93.05 smid" } @techreport{hr-acmcsad-96 , author = "T. H. Hopp and C. P. Reeve" , title = "An algorithm for computing the minimum covering sphere in any dimension" , institution = "National Institute of Standards and Technology" , year = "1996" , number = "NISTIR 5831" } @inproceedings{sw-usoc-2001, author = "T. Szab{\'o} and E. Welzl", title = "Unique sink orientations of cubes", booktitle= "Proc. 42nd annual IEEE Symposium on Foundations of Computer Science (FOCS)", pages = "547--555", year = "2001", bibdate = "Fri Feb 22 06:31:27 MST 2002", bibsource = "http://ieeexplore.ieee.org/" } @misc{prisme-cgal-2.3 , key = "CGAL" , url = "http://www.cgal.org" , editor = "Andreas Fabri and Bernd G{\"a}rtner and Susan Hert and Shai Hirsch Michael Hoffmann and Lutz Kettner and Dmitrii Pasechnik and Sylvain Pion and Remco Veltkamp and Mariette Yvinec " , title = "The {CGAL} Reference Manual" , note = "Release 2.3" , year = 2001 , month = "August" } @book{bss-np-79 , author = "M. S. Bazaraa and H. D. Sherali and C. M. Shetty" , title = "Nonlinear programming: theory and applications" , publisher = "Wiley" , year = 1979 } @book{b-g-87 , author = "M. Berger" , title = "Geometry (vols.\ 1--2)" , publisher = "Springer-Verlag" , year = 1987 , succeeds = "b-g-77" , update = "96.09 devillers" } @article{m-rjmt-92 , author = "J. M{\o}ller" , title = "Random {Johnson-Mehl} tessellations" , journal = "Adv. Appl. Prob." , volume = "24" , year = "1992" , pages = "814--844" } @book{r-ca-70 , author="R.T. Rockafellar" , title="Convex Analysis" , publisher="Princeton University press" , year=1970 } @article{lvbl-asocp-98 , author = "M. S. Lobo and L. Vandenberghe and S. Boyd and H. Lebret" , title = "Applications of second-order cone programming" , journal = "Linear Algebra and its Applications" , volume = "284" , year = "1998" , pages = "193--228" } @book{psu-mnp-88 , author = "A. L. Peressini and F. E. Sullivan and J. J. Uhl" , title = "The mathematics of nonlinear programming" , series = "Undergraduate Texts in Mathematics" , publisher = "Springer-Verlag" , year = 1988 , update = "97.03 gaertner+salinger" } @inproceedings{bcd-acchs-92 , author = "J. D. Boissonat and A. C{\'e}r{\'e}zo and J. Duquesne" , title = "An Algorithm for Constructing the Convex Hull of a Set of Spheres in Three Dimensional Space" , booktitle = "Abstracts 8th European Workshop Comput. Geom." , nickname = "CG '92" , site = "Utrecht" , publisher = "Utrecht University" , year = 1992 , pages = "51--53" , update = "00.03 bibrelex" } @article{d-ltatt-84 , author = "M. E. Dyer" , title = "Linear time algorithms for two- and three-variable linear programs" , journal = "SIAM J. Comput." , volume = 13 , year = 1984 , pages = "31--45" , keywords = "linear programming" } @inproceedings{d-ccpac-92 , author = "M. E. Dyer" , title = "A class of convex programs with applications to computational geometry" , booktitle = "Proc. 8th Annu. ACM Sympos. Comput. Geom." , year = 1992 , pages = "9--15" , cites = "c-sagcp-88, c-lpot-86, c-lvalp-88, dk-ladsc-85, d-mstia-86, gls-gaco-88, j-ba1-85, m-lpltw-84, m-bsb-89, m-mpta-86, p-mse-84, r-fpade-88, sw-cblpr-92, w-sedbe-91a, ZZZ" , update = "97.11 bibrelex, 97.03 agarwal" } @article{gw-ssl-00 , author = "Bernd G{\"a}rtner and Emo Welzl" , title = "On a simple sampling lemma" , journal = "Electronic Notes in Theoretical Computer Science" , volume = "31" , year = "2000" , url = "citeseer.nj.nec.com/gartner00simple.html" } @incollection{gw-eie-01 , author = "Bernd G{\"a}rtner and Emo Welzl" , title = "Explicit and Implict Enforcing -- Randomized Optimization" , booktitle= "Computational Discrete Mathematics" , series ="LNCS" , publisher="Springer-Verlag" , volume = "2122" , year = "2001" , pages = "25--46" } @inproceedings{gs-eegqp-00 , author = "Bernd G{\"a}rtner and Svend Sch{\"o}nherr" , title = "An Efficient, Exact, and Generic Quadratic Programming Solver for Geometric Optimization" , booktitle = "Proc. 16th Annu. ACM Sympos. Comput. Geom." , year = 2000 , pages = "110--118" , update = "00.11 jones" } @article{g-saaop-92 , author = "B. G{\"a}rtner" , title = "A subexponential algorithm for abstract optimization problems" , journal = "SIAM J. Comput," , volume = 24 , number = 5 , year = 1995 , pages = "1018--1035" } @book{cg-gr-67 , author = "H. S. M. Coxeter and S. L. Greitzer" , title = "Geometry Revisited" , publisher = "Mathematical Association of America" , address = "Washington, DC" , year = 1967 } @inproceedings{r-odtr-91 , author = "V. T. Rajan" , title = "Optimality of the {Delaunay} triangulation in {$R^{d}$}" , booktitle = "Proc. 7th Annu. ACM Sympos. Comput. Geom." , year = 1991 , pages = "357--363" , keywords = "Delaunay triangulation" , precedes = "r-odtr-94" , cites = "a-vds-88, b-vdch-79, e-acg-87, es-vda-86, e-atccd-89, f-savd-87, gs-pmgsc-85, l-gtgac-72, ps-cgi-85, sh-cpp-75, s-cg-78, sntm-amgus-90, ZZZ" , update = "00.03 bibrelex, 97.11 bibrelex" } @techreport{e-was-92 , author = "H. Edelsbrunner" , title = "Weighted alpha shapes" , type = "Technical {Report}" , number = "UIUCDCS-R-92-1760" , institution = "Dept. Comput. Sci., Univ. Illinois" , address = "Urbana, IL" , year = 1992 , update = "98.03 bibrelex" } @article{em-sstcd-90 , author = "H. Edelsbrunner and E. P. M{\"u}cke" , title = "Simulation of simplicity: {A} technique to cope with degenerat\e cases in geometric algorithms" , journal = "ACM Trans. Graph." , volume = 9 , number = 1 , year = 1990 , pages = "66--104" , succeeds = "em-sstcd-88" , update = "98.07 agarwal+tamassia" } @article{s-fpavp-80 , author = "J. T. Schwartz" , title = "Fast Probabilistic Algorithms for Verification of Polynomial Identities" , journal = "Journal of the Association of Computing Machinery" , volume = 27 , number = 4 , year = 1980 , pages = "701--717" } @techreport{em-tdas-92 , author = "H. Edelsbrunner and E. P. M{\"u}cke" , title = "Three-dimensional alpha shapes" , type = "Manuscript" , number = "UIUCDCS-R-92-1734" , institution = "Dept. Comput. Sci., Univ. Illinois" , address = "Urbana-Champaign, IL" , year = 1992 , update = "98.03 bibrelex, 97.11 bibrelex" } @techreport{ke-ppawvd-01 , author = "M. Karavelas and I. Emiris" , title = "Predicates for the planar additively weighted {Voronoi} diagram" , institution = "Sophia-Antipolis" , year = "2002" , type = "ECG Technical Report" , number = "ECG-TR-122201-01" } @article{em-tdas-94 , author = "H. Edelsbrunner and E. P. M{\"u}cke" , title = "Three-dimensional Alpha Shapes" , journal = "ACM Trans. Graph." , volume = 13 , number = 1 , month = jan , year = 1994 , pages = "43--72" , url = "ftp://cs.uiuc.edu/pub/edels/geometry/shapes-94.tar.Z" , comments = "Software in \path|ftp://cs.uiuc.edu/pub/edels/geometry/alpha-2\.1a.tar.Z|" , update = "94.09 orourke" } @inproceedings{tc-sradsas-98 , author = "M. Teichmann and M. Capps" , title = "Surface reconstruction with anisotropic density-scaled alpha-shapes" , booktitle = "IEEE Visualization '98 Proceedings" , publisher = "ACM/SIGGRAPH Press" , address = "San Francisco, CA" , month = oct , year = 1998 , pages = "67--72" } @book{psu-mnp-93 , author = "A.~L. Peressini, F.~E. Sullivan and J.~J. Uhl, Jr." , title = "The mathematics of nonlinear programming" , publisher = "Springer Verlag" , address = "New York" , year = 1993 , note = "ISBN 0-387-96614-5" } @book{b-a-91 , author = "C. Blatter" , title = "Analysis I" , publisher = "Springer Verlag" , address = "Berlin" , year = 1991 , note = "ISBN 3-540-54239-6" } @book{s-opg-91 , author = "J. Stolfi" , title = "Oriented Projective Geometry" , publisher = "Academic Press, Inc." , address = "San Diego" , year = 1991 , note = "ISBN 0-12-672025-8" } @article{mt-pgfa-96 , author = "R. Mohr and B. Triggs" , title = "Projective Geometry for Image Analysis" , year = 1996 , url = "http://www.inrialpes.fr/movi/people/Triggs/isprs96/isprs96.html" } @book{g-cgte-71 , author = "L. Gaal" , title = "Classical Galois Theory, with Examples" , publisher = "Chelsea Publishing Company" , address = "New York" , year = 1971 , note = "ISBN 0-8284-0268-X" } @book{c-ccant-96 , author = "H. Cohen" , title = "A Course in Computational Algebraic Number Theory" , publisher = "Springer Verlag" , address = "New York" , year = 1996 , note = "ISBN 3-540-55640-0" } @book{a-a-93 , author = "M. Artin" , title = "Algebra" , publisher = "Birkh{\"a}user Verlag" , address = "Basel" , year = 1993 , note = "ISBN 3-7643-2927-0" } @book{bjn-baa-94 , author = "P.~B. Bhattacharya, S.~K. Jain and S.~R. Nagpaul" , title = "Basic Abstract Algebra" , publisher = "Cambridge University Press" , address = "New York" , year = 1994 , note = "ISBN 0-521-46629-6" } @book{nh-adsagg-93 , author = "J. Nievergelt and K. H. Hinrichs" , title = "Algorithms \& Data Structures: with applications to graphics and geometry" , publisher = "Prentice Hall" , address = "Englewood Cliffs, New Jersey" , year = 1993 , note = "ISBN 0-13-489428-6" } @book{c-acpsi-92 , author = "J. O. Coplien" , title = "Advanced C++ programming styles and idioms" , publisher = "Addison Wesley" , year = 1992 , note = "ISBN 0-201-54855-0" } @book{is-isoiec14882 , author = "Information Technology Industry Council" , title = "International Standard ISO/IEC 14882: Programming Languages --- C++" , publisher = "American National Standards Institute" , year = 1998 } @techreport{gs-seefe-97t , author = "B. G{\"a}rtner and S. Sch{\"o}nherr" , title = "Smallest enclosing ellipses---fast and exact" , type = "Technical {Report}" , institution = "Free University Berlin" , address = "Berlin, Germany" , year = 1997 , update = "98.07 bibrelex" } @article{s-sacse-91 , author = "S. Skyum" , title = "A simple algorithm for computing the smallest enclosing circle\" , journal = "Inform. Process. Lett." , volume = 37 , year = 1991 , pages = "121--125" , keywords = "computational geometry, Voronoi diagrams, convex polygons" , abstract = "Presented is a simple $O(n \log n)$ algorithm for computing the smallest enclosing circle of a convex polygon. It can be easily extended to algorithms that compute the farthest- and the closest-point Voronoi diagram of a convex polygon within the same time bound. (Author abstract) 4 Refs." } @incollection{w-sedbe-91a , author = "Emo Welzl" , title = "Smallest enclosing disks (balls and ellipsoids)" , editor = "H. Maurer" , booktitle = "New Results and New Trends in Computer Science" , series = "Lecture Notes Comput. Sci." , volume = 555 , publisher = "Springer-Verlag" , year = 1991 , pages = "359--370" , succeeds = "w-sedbe-91" , update = "98.03 mitchell, 94.01 rote, 93.09 matousek" } @article{s-qgs-57 , author = "J. J. Sylvester" , title = "A question on the geometry of situation" , journal = "Quart. J. Math." , volume = 1 , year = 1857 , pages = 79 } @article{m-lpltw-84 , author = "N. Megiddo" , title = "Linear programming in linear time when the dimension is fixed" , journal = "J. ACM" , volume = 31 , year = 1984 , pages = "114--127" , keywords = "design of algorithms, linear programming, worst-case analysis, prune-and-search" } @article{m-bsb-89 , author = "N. Megiddo" , title = "On the ball spanned by balls" , journal = "Discrete Comput. Geom." , volume = 4 , year = 1989 , pages = "605--610" } @mastersthesis{z-kekib-91 , author = "J. Ziegler" , title = "Kleinste einschlie{\ss}ende Kugel und ihre Berechnung" , school = "Universit{\"a}t des Saarlands, Saarbr{\"u}cken" , year = 1991 , note = "Diplomarbeit" } @phdthesis{s-qpgotia-2002 , author = "S. Sch{\"o}nherr" , title = "Quadratic programming in geometric optimization: theory, implementation, and applications" , school = "ETH Z{\"u}rich" , year = 2002 , note = "PhD thesis" } @mastersthesis{f-sebb-01 , author = "K. Fischer" , title = "The smallest enclosing ball of balls" , school = "ETH Z{\"u}rich" , year = 2001 , note = "Diplomarbeit" } @techreport{f-tnmb-01 , author = "K. Fischer" , title = "Two notes on the miniball of balls" , type = "Manuscript" , institution = "ETH Z{\"urich}" , year = 2001 , note = "CGC mid-term project" } @book{c-lp-83 , author = "V. Chv{\'a}tal" , title = "Linear programming" , publisher = "W. H. Freeman" , address = "New York, NY" , year = 1983 } @phdthesis{Will , author = "Hans-Martin Will" , title = "Computation of additively weighted Voronoi cells for applications in molecular biology" , institution ="Institute for Theoretical Computer Science" , school= "ETH Z{\"u}rich" , year="1998" } @misc{s-pc-97 , author = "R. Seidel" , howpublished= "e-mail communication" , year = 1997 } @article{w-pc-00 , author = "R. Willcocks" , note = "Personal communication to K. Fischer" , month = "September" , year = 2000 } @manual{nu-lmum-95 , author = "S. N{\"a}her and C. Uhrig" , title = "The {LEDA} Manual User Manual" , year = 1995 , update = "97.11 bibrelex" } @book{asi-plr-99 , author = "{Adobe Systems Incorporated}" , title = "{PostScript} Language Reference" , publisher = "Addison-Wesley" , address = "Reading, MA, USA" , edition = "Third" , pages = "xii + 897" , year = "1999" , ISBN = "0-201-37922-8" } @inproceedings{g-frseb-99 , author = "B. G{\"a}rtner" , title = "Fast and Robust Smallest Enclosing Balls" , booktitle = "Proc. 7th Annual European Symposium on Algorithms (ESA)" , series = "Lecture Notes Comput. Sci." , volume = 1643 , publisher = "Springer-Verlag" , year = 1999 , pages = "325--338" } @book{null , author = "No references" , title = "Sorry" } @techreport{fn-ppwrts-02 , author = "K. Fischer" , title = "The power of a point w.r.t.~a sphere" , type = "File note" , number = "2002-05-07-power" , institution = "ETH Z{\"urich}" , year = 2002 } @techreport{fn-mi-02 , author = "K. Fischer" , title = "The miniball and inversion" , type = "File note" , number = "2002-09-10-mbb-inversion" , institution = "ETH Z{\"urich}" , year = 2002 } @techreport{fn-mopob-02 , author = "K. Fischer" , title = "The miniball and one point on the boundary" , type = "File note" , number = "2002-10-24-mbb-1ptb" , institution = "ETH Z{\"urich}" , year = 2002 }