[Ame1]

N. Amenta, Helly-type theorems and generalized linear programming,*Discrete Comput. Geom.*,**12** (1994), 241–261.

[Ame2]

N. Amenta, Bounded boxes, Hausdorff distance, and a new proof of an interesting Helly-type theorem,*Proc. 10th Annual ACM Symposium on Computational Geometry*, 1994, pp. 340–347.

[Bel]

D. E. Bell, A theorem concerning the integer lattice,*Stud. Appl. Math.*,**56** (1977), 187–188.

[ChM]

B. Chazelle and J. Matoušek, On linear-time deterministic algorithms for optimization problems in fixed dimensions, Technical Report B 92-18, Dept. of Mathematics, Freie Universität Berlin (1992); also*Proc. 4th SIAM-ACM Symposium on Discrete Algorithms*, 1993, pp. 281–290.

[Cla1]

K. L. Clarkson, Linear programming in*O*(*n* × 3*d*
^{2}) time,*Inform. Process. Lett.*,**22** (1986), 21–24.

[Cla2]

K. L. Clarkson, New applications of random sampling in computational geometry,*Discrete Comput. Geom.*,**2** (1987), 195–222.

[Cla3]

K. L. Clarkson, Las Vegas algorithms for linear and integer programming when the dimension is small,*J. Assoc. Comput. Mach.*,**42** (1995), 488–499.

[DLL]

L. Danzer, D. Laugwitz, and H. Lenz, Über das Löwnersche Ellipsoid und sein Analogon unter den einem Eikörper eingeschriebenen Ellipsoiden,*Arch. Math.*,**8** (1957), 214–219.

[Dan]

D. B. Dantzig,*Linear Programming and Extensions*, Princeton University Press, Princeton, NJ, 1963.

[Dör]

J. Dörflinger, Approximation durch Kreise: Algorithmen zur Ermittlung der Formabweichung mit Koordinatenmeßgeräten, Diplomarbeit, Universiät Ulm, 1986.

[Dye1]

M. E. Dyer, On a multidimensional search technique and its application to the Euclidean one-center problem,*SIAM J. Comput.*,**15** (1986), 725–738.

[Dye2]

M. E. Dyer, A class of convex programs with applications to computational geometry,*Proc. 8th Annual ACM Symposium on Computational Geometry*, 1992, pp. 9–15.

[DyF]

M. E. Dyer and A. M. Frieze, A randomized algorithm for fixed-dimensional linear programming,*Math. Programming*,**44** (1989), 203–212.

[Gär1]

B. Gärtner, personal communication (1991).

[Gär2]

B. Gärtner, A subexponential algorithm for abstract optimization problems,*SIAM J. Comput.*,**24** (1995), 1018–1035.

[Juh]

F. Juhnke, Volumenminimale Ellipsoidüberdeckungen,*Beitr. Algebra Geom.*,**30** (1990), 143–153.

[Jun]

H. Jung, Über die kleinste Kugel, die eine räumliche Figur einschließt,*J. Reine Angew. Math.*,**123** (1901), 241–257.

[Kal]

G. Kalai, A subexponential randomized simplex algorithm,*Proc. 24th ACM Symposium on Theory of Computing*, 1992, pp. 475–482.

[KAR]

N. Karmarkar, A new polynomial-time algorithm for linear programming,*Combinatorica*,**4** (1984), 373–395.

[Kha]

L. G. Khachiyan, Polynomial algorithm in linear programming,*U.S.S.R. Comput. Math. and Math. Phys.*,**20** (1980), 53–72.

[KlM]

V. Klee and G. J. Minty, How good is the simplex algorithm, in*Inequalities III*, (O. Shisha, ed.), Academic Press, New York, 1972, pp. 159–175.

[Mat1]

J. Matoušek, Lower bounds for a subexponential optimization algorithm,*Random Structures Algorithms*,**5** (1994), 591–607.

[Mat2]

J. Matoušek, On geometric optimization with few violated constraints,*Proc. 10th Annual ACM Symposium on Computational Geometry*, 1994, pp. 312–321.

[Meg1]

N. Megiddo, Linear time algorithms for linear time programming in*R*
^{3} and related problems,*SIAM J. Comput.*,**12** (1983), 759–776.

[Meg2]

N. Megiddo, Linear programming in linear time when the dimension is fixed,*J. Assoc. Comput. Mach.*,**31** (1984), 114–127.

[Meg3]

N. Megiddo, A note on subexponential simplex algorithms, manuscript (1992).

[d'Oi]

J.-P. D'Oignon, Convexity in cristallographie lattices,*J. Geom.*,**3** (1973), 71–85.

[Pos]

M. J. Post, Minimum spanning ellipsoids,*Proc. 16th Annual ACM Symposium on Theory of Computing*, 1984, pp. 108–116.

[Rot]

G. Rote, personal communication (1991).

[Sca]

H. E. Scarf, An observation on the structure of production sets with indivisibilities,*Proc. Nat. Acad. Sci. U.S.A.*,**74** (1977), 3637–3641.

[Sei]

R. Seidel, Low dimensional linear programming and convex hulls made easy,*Discrete Comput. Geom.*,**6** (1991), 423–434.

[ShW]

M. Sharir and E. Welzl, A combinatorial bound for linear programming and related problems,*Proc. 9th Symposium on Theoretical Aspects of Computer Science*, Lecture Notes in Computer Science, 577, Springer-Verlag, Berlin, 1992, pp. 569–579.

[Syl]

J. J. Sylvester, A question in the geometry of situation,*Quart. J. Math.*,**1** (1857), 79.

[Wel]

E. Welzl, Smallest enclosing disks (balls and ellipsoids),*New Results and New Trends in Computer Science* (H. Maurer, ed.), Lecture Notes in Computer Science, Vol. 555, Springer-Verlag, Berlin, 1991, pp. 359–370.