1.

F. Aurenhammer, Power diagrams: Properties, algorithms and applications, Rep. F120, IIG, Tech. Univ. Graz, Austria, 1983.

Google Scholar2.

F. P. Ash and E. D. Boler, Generalized Dirichlet tesselations, to be published.

3.

F. Aurenhammer and H. Edelsbrunner, An optimal algorithm for constructing the weighted Voronoi diagram in the plane, Pattern Recognition 17 (1984), 251–257.

MathSciNetCrossRefMATHGoogle Scholar4.

B. Bhattacharya, An algorithm for computing order

*k* Voronoi diagrams in the plane, CS Dept. Tech. Rep. TR. 83-9, Simon Fraser Univ., Burnaby B.C., 1983.

Google Scholar5.

A. Bowyer, Computing Dirichlet tesselations, The Computer Journal 24 (1981), 162–166.

MathSciNetCrossRefGoogle Scholar6.

K. Q. Brown, Fast intersection of half spaces, CS Dept. Rep. CMU-CS-78-129, CMU, Pittsburgh PA, 1978.

Google Scholar7.

K. Q. Brown, Voronoi diagrams from convex hulls, Info. Proc. Let. 9 (1979), 223–228.

CrossRefGoogle Scholar8.

K. Q. Brown, Geometric transforms for fast geometric algorithms, Ph.D. thesis, CS Dept. Rep. CMU-CS-80-101, CMU, Pittsburgh PA, 1980.

Google Scholar9.

L. P. Chew and R. L. Drysdale, III, Voronoi diagrams based on convex distance functions, Proc. of the ACM Symp. on Computational Geometry, 1985, 235–244.

10.

R. Cole and C. K. Yap, Geometric retrieval problems, Proc. of the 24th IEEE Symp. on Foundations of Computer Science, 1983, 112–121.

11.

F. Dehne, An optimal algorithm to construct all Voronoi diagrams for*k* nearest neighbor searching in the Euclidean plane, Proc. of the 20th Annual Allerton Conf. on Communication, Control, and Computing, 1982.

12.

R. L. Drysdale, III, Generalized Voronoi diagrams and geometric searching, Ph.D. thesis, CS Dept. Rep. STAN-CS-79-705, Stanford Univ., Stanford, CA, 1979.

Google Scholar13.

H. Edelsbrunner, Arrangements and Geometric Computations, forthcoming book.

14.

H. Edelsbrunner, J. O'Rourke, and R. Seidel, Constructing arrangements of lines and hyperplanes with applications, Proc. 24th Symp. on Foundations of Computer Science, 1983, 83–91 (to appear in SIAM J. Computing).

15.

H. Edelsbrunner and E. Welzl, On the number of line-separations of a finite set in the plane, Rep. F97, IIG, Tech. Univ. Graz, Austria, 1982 (to appear in J. Combin. Theory, Ser. A).

Google Scholar16.

P. Erdös, L. Lovasz, A. Simmons, and E. G. Straus, Dissection graphs of planar point sets, in A Survey of Combinatorial Theory, J. N. Srivastava et al., eds., North-Holland, Amsterdam, 1973.

Google Scholar17.

B. Grünbaum, Arrangements of hyperplanes, Conf. Numerantium III, Louisiana Conf. on Comb., Graph Theory and Computing, 1971, 41–106.

18.

B. Grünbaum, Arrangements and spreads, Reg. Conf. Series in Math., AMS, Providence, 1972.

19.

H. Imai, M. Iri, and K. Murota, Voronoi diagrams in the Laguerre geometry and its application, SIAM J. Computing, to appear.

20.

D. G. Kirkpatrick, Efficient computation of continuous skeletons, Proc. of the 20th IEEE Symp. on Foundations of Computer Science, 1979, 18–27.

21.

D. T. Lee, On finding

*k*-nearest neighbors in the plane, M.S. thesis, Coordinated Science Lab., Rep. R-728, Univ. of Illinois, Urbana Ill., 1976.

Google Scholar22.

D. T. Lee, Two dimensional Voronoi diagrams in the*L*
_{p}-metric, J. ACM, Oct. 604–618 (1980).

23.

D. T. Lee and R. L. Drysdale, III, Generalized Voronoi diagrams in the plane, SIAM J. Computing, 10 (1981), 73–87.

MathSciNetCrossRefMATHGoogle Scholar24.

D. T. Lee and C. K. Wong, Voronoi diagrams in

*L*
_{1}- (

*L*
_{∞}-) metrics with 2-dimensional storage applications, SIAM J. Computing, 9 (1980), 200–211.

MathSciNetCrossRefMATHGoogle Scholar25.

P. McMullen, The maximum number of faces of a convex polytope, Mathematika 17 (1970), 179–184.

MathSciNetCrossRefMATHGoogle Scholar26.

A. Mandel, Topology of oriented matroids, Ph.D. thesis, Dept. of Combinatorics and Optimization, Univ. of Waterloo, Waterloo, Ont., 1981.

Google Scholar27.

I. Paschinger, Konvexe Polytope und Dirichletsche Zellenkomplexe, Math. Inst., Univ. Salzburg, Austria, Arbeitsbericht 1–2, 1982.

MATHGoogle Scholar28.

F. P. Preparata and S. J. Hong, Convex hulls of finite sets of points in two and three dimensions, C. ACM 20 (1977), 87–93.

MathSciNetCrossRefMATHGoogle Scholar29.

F. P. Preparta and D. E. Muller, Finding the intersection of

*n* halfspaces in time

*O* (

*n* log

*n*), Theore. Comput. Sci. 8 (1979), 45–55.

CrossRefMATHGoogle Scholar30.

R. Seidel, A convex hull algorithm optimal for point sets in even dimensions, Rep. 81-14, Dept. of CS, Univ. of BC, Vancouver B.C., 1981.

Google Scholar31.

M. I. Shamos and D. Hoey, Closest-point problems, Proc. of the 17th IEEE Symp. on Foundations of Computer Science, 208–215, 1975.

32.

M. Sharir, and D. Leven, Intersection problems and application of Voronoi diagrams, in Advances in Robotics, Vol. 1: Algorithmic and Geometric Aspects of Robotics, J. Schwartz and C. K. Yap, eds., Lawrence Erlbaum Associates Inc. (to appear).

33.

D. F. Watson, Computing the

*n*-dimensional Delaunay triangulation with applications to Voronoi polytopes, Comput. J. 24 (1981), 167–172.

MathSciNetCrossRefGoogle Scholar34.

C. K. Yap, An

*O* (

*n* log

*n*) algorithm for the Voronoi diagram of a set of simple curve segments, manuscript, Courant Institute of Math. Sciences, NYU, New York, NY, 1984.

Google Scholar35.

T. Zaslavsky, Facing up to arrangements: Face-count formulas for partitions of space by hyperplanes, Memoirs AMS 154 (1975).