Sphere-separable partitions of multi-parameter elements

Discrete Applied Mathematics

Volumn 156, Issue 6, 2008, Pages 838-845

  Golany, Boaz ^a   Hwang, Frank K ^b   Rothblum, Uriel G ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

Author keywords

Combinatorial optimization; Partitions; Polynomial bounds; Separation

Indexed keywords

COMBINATORIAL OPTIMIZATION; POLYNOMIALS; PROBLEM SOLVING; VECTORS;

OPTIMAL SOLUTION; PARTITIONS; POLYNOMIAL BOUNDS;

PARAMETER ESTIMATION;

EID: 39449089112     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2006.06.012     Document Type: Article

References (13)

1. Alon N., and Onn S. Separable partitions. Discrete Appl. Math. 91 (1999) 39-51
2. Aviram S., Lev-Tov N., Onn S., and Rothblum U.G. Vertex characterization of partition polytopes of planar point sets. Discrete. Appl. Math. 125 (2002) 1-15
3. Barnes E.R., Hoffman A.J., and Rothblum U.G. Optimal partitions having disjoint convex and conic hulls. Math. Programming 54 (1992) 69-86
4. Boros E., and Hammer P.L. On clustering problems with connected optima in Euclidean spaces. Discrete Math. 75 (1989) 81-88
5. Boros E., and Hwang F.K. Optimality of nested partitions and its applications to cluster analysis. SIAM J. Optam. 6 (1995) 1153-1162
6. Fisher W.D. On grouping for maximum homogeneity. J. Amer. Statist. Assoc. 53 (1958) 789-798
7. Hassin M., and Rubinstein S. Approximation algorithms for the metric maximum clustering problem with given cluster sizes. Oper. Res. Lett. 31 (2003) 179-184
8. Hwang F.K., Lee J.S., Liu Y.C., and Rothblum U.G. Sortability of vector partitioning. Discrete. Math. 263 (2003) 129-142
9. Hwang F.K., and Mallows C.L. Enumerating consecutive and nested partitions. J. Combin. Theory Ser. A 70 (1995) 323-333
10. Hwang F.K., Onn S., and Rothblum U.G. A polynomial time algorithm for shaped partition problems. SIAM J. Optam. 10 (1999) 70-81
11. Hwang F.K., and Rothblum U.G. Directional-quasi-convexity, Schur-convexity and the optimality of consecutive partitions. Math. Oper. Res. 21 (1996) 540-554
12. F.K. Hwang, U.G. Rothblum, Partitions: Optimality and Clustering, 2007, forthcoming.
13. Onn S., and Schulman L.J. The vector partition problem for convex objective functions. Math. Oper. Res. 26 (2001) 583-590