LEADER 04987oam 2200529 450 001 9910814172003321 005 20190911112728.0 010 $a981-4412-35-X 035 $a(OCoLC)844311189 035 $a(MiFhGG)GVRL8RFH 035 $a(EXLCZ)992670000000372466 100 $a20100928h20132013 uy 0 101 0 $aeng 135 $aurun|---uuuua 181 $ctxt 182 $cc 183 $acr 200 10$aPartitions $eoptimality and clustering. Vol. II, Multi-parameter /$fFrank K. Hwang, National Chiao-Tung University, Taiwan, Uriel G. Rothblum, Technion, Israel, Hong-Bin Chen, Academia Sinica, Taiwan 210 $aSingapore $cWorld Scientific Pub. Co.$d2013 210 1$aNew Jersey :$cWorld Scientific,$d[2013] 210 4$d?2013 215 $a1 online resource (x, 291 pages) $cillustrations (some color) 225 0 $aPartitions : optimality and clustering ;$vv. 2 225 0$aSeries on applied mathematics ;$vv. 20 300 $aDescription based upon print version of record. 311 $a981-4412-34-1 320 $aIncludes bibliographical references and index. 327 $aContents; Preface; 1. Bounded-Shape Sum-Partition Problems: Polyhedral Approach; 1.1 Linear Objective: Solution by LP; Testing If a Vector (say A ) is a Vertex of a given Bounded- Shape Partition Polytope; Solution of Bounded-Shape Partition Problems with Linear Objective Function; 1.2 Enumerating Vertices of the Partition Polytopes and Corresponding Partitions Using Edge-Directions; Enumerating Vertices of Bounded-Shape Partition Polytopes along with Corresponding Partitions Using Edge-Directions; Single-Size Problems 327 $aEnumerating the Facets of a Constrained-Shape Partition Polytope Using Generic Partitions (along with Supporting Hyperplanes)1.3 Representation, Characterization and Enumeration of Vertices of Partition Polytopes: Distinct Partitioned Vectors; Testing if a Vector A is a Vertex of the Bounded-Shape Partition Polytope When the Columns of A are Nonzero and Distinct; Testing if a Vector A is a Vertex of the Bounded-Shape Partition Polytope When the Columns of A are Distinct, but Contain the Zero Vector; Mean-Partition Problems 327 $a1.4 Representation, Characterization and Enumeration of Vertices of Partition Polytopes: General CaseTesting if a Vector A is a Vertex of the Bounded-Shape Partition Polytope; Appendix A; 2. Constrained-Shape and Single-Size Sum-Partition Problems: Polynomial Approach; 2.1 Constrained-Shape Partition Polytopes and (Almost-) Separable Partitions; Testing for a Point of a Finite Set to be a Vertex of the Convex Hull of that Set; Testing for (Almost) Separability of Partitions; Enumerating the Vertices of Constrained-Shape and Bounded-Shape Partition Polytopes with Underlying Matrix A 327 $aGenerating the Vertices of Bounded-Shape and Constrained- Shape Partition Polytopes2.2 Enumerating Separable and Limit-Separable Partitions of Constrained-Shape; Enumerating all Separable 2-Partitions when A is Generic; Enumerating all Separable p-Partitions when A is Generic; Computing Generic Signs; Enumerating all A-Limit-Separable Partitions; Enumerating all A-Separable Partitions; Solving Constrained-Shape Partition Problems with f(·) (Edge-)Quasi-Convex by Enumerating Limit-Separable Partitions 327 $aEnumerating the Vertices of Constrained-Shape Partition Polytopes Using Limit-Separable PartitionsEnumerating all Almost-Separable 2-Partitions; Enumerating all Almost-Separable p-Partitions; 2.3 Single-Size Partition Polytopes and Cone-Separable Partitions; Testing for Cone-Separability of Finite Sets; Testing for Cone-Separability of Partitions; 2.4 Enumerating (Limit-)Cone-Separable Partitions; Enumerating All Cone-Separable Partitions when [0,A] is Generic; Enumerating All Cone-Separable Partitions when d 2 and A has no Zero Vectors 327 $aEnumerating All A-Limit-Cone-Separable Partitions when d > 2 330 $aThe need for optimal partition arises from many real-world problems involving the distribution of limited resources to many users. The ""clustering"" problem, which has recently received a lot of attention, is a special case of optimal partitioning. This book is the first attempt to collect all theoretical developments of optimal partitions, many of them derived by the authors, in an accessible place for easy reference. Much more than simply collecting the results, the book provides a general framework to unify these results and present them in an organized fashion. Many well-known practical p 410 0$aSeries on applied mathematics ;$vv. 20. 606 $aPartitions (Mathematics) 615 0$aPartitions (Mathematics) 676 $a512.73 700 $aHwang$b Frank$0736498 702 $aRothblum$b Uriel G. 702 $aChen$b Hongbin 801 0$bMiFhGG 801 1$bMiFhGG 906 $aBOOK 912 $a9910814172003321 996 $aPartitions$94050287 997 $aUNINA