论文信息 - Diameter partitioning

Diameter partitioning

We discuss the problem of partitioning a set of points into two subsets with certain conditions on the diameters of the subsets and on their cardinalities. For example, we give anO(n2 logn) algorithm to find the smallestt such that the set can be split into two equal cardinality subsets each of which has diameter at mostt. We also give an algorithm that takes two pairs of points (x, y) and (s, t) and decides whether the set can be partitioned into two subsets with the respective pairs of points as diameters.

David Avis | D. Avis

[1] Herbert Edelsbrunner,et al. On the Number of Line Separations of a Finite Set in the Plane , 1985, J. Comb. Theory, Ser. A.

[2] T. Ibaraki,et al. The Computational Complexity of the m -Center Problems on the Plane , 1981 .

[3] F. Frances Yao,et al. A 3-space partition and its applications , 1983, STOC.

[4] P. Erdös,et al. Dissection Graphs of Planar Point Sets , 1973 .

[5] Arnold L. Rosenberg,et al. Stabbing line segments , 1982, BIT.

[6] David P. Dobkin,et al. Space Searching for Intersecting Objects , 1984, FOCS.

[7] David Avis. Non-Partitionable Point Sets , 1984, Inf. Process. Lett..

[8] Kenneth Jay Supowit,et al. Topics in Computational Geometry , 1981 .

[9] Dan E. Willard,et al. Polygon Retrieval , 1982, SIAM journal on computing (Print).

[10] David P. Dobkin,et al. Space Searching for Intersecting Objects , 1987, J. Algorithms.

[11] David Avis,et al. Space Partitioning and its Application to Generalized Retrieval Problems , 1985, FODO.

[12] Robert J. Fowler,et al. Optimal Packing and Covering in the Plane are NP-Complete , 1981, Inf. Process. Lett..

[13] Alfred V. Aho,et al. The Design and Analysis of Computer Algorithms , 1974 .

[14] David Avis,et al. On the partitionability of point sets in space (preliminary report) , 1985, SCG '85.