Contents -- 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 -- Enumerating 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 -- 1.4 Representation, Characterization and Enumeration of Vertices of Partition Polytopes: General Case -- Testing 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 -- Generating the Vertices of Bounded-Shape and Constrained- Shape Partition Polytopes -- 2.2 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 -- Enumerating the Vertices of Constrained-Shape Partition Polytopes Using Limit-Separable Partitions -- Enumerating 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 -- Enumerating All A-Limit-Cone-Separable Partitions when d > 2 -- Enumerating All A-Cone-Separable Partitions when A has no Zero Vectors -- Enumerating All A-Cone-Separable Partitions when A has Zero Vectors -- Solving Single-Size Partition Problems with f(·) (Edge-) Quasi-Convex by Enumerating Limit-Cone-Separable Partitions -- Enumerating the Vertices of Single-Size Partition Polytopes Using Limit-Cone-Separable Partitions -- 3. Partitions over Multi-Parameter Spaces: Combinatorial Structure -- 3.1 Properties of Partitions -- 3.2 Counting and Enumerating Partition Classes of Single-Size -- 3.3 Consistency and Sortability of Particular Partition- Properties -- 4. Clustering Problems over Multi-parameter Spaces -- 4.1 Geometric Properties of Optimal Partitions -- 4.2 Geometric Properties of Optimal Partitions for d = 2 -- 5. Sum-Multipartition Problems over Single-Parameter Spaces -- 5.1 Multipartitions.

5.2 Single-Multishape Multipartition Polytopes -- 5.3 Constrained-Multishape Multipartition Polytopes -- 5.4 Combinatorial Properties of Multipartitions -- 5.5 Constrained-Multishape Multipartition Problems with Asymmetric Schur Convex Objective: Optimization over Multipartition Polytopes -- Solution of Single-Multishape Sum Multipartition Problems with f Asymmetric Schur Convex by Enumerating Monotone Multipartitions -- Solution of Constrained-Multishape Sum Multipartition Problems with f Asymmetric Schur Convex by Enumerating Monotone Multipartitions -- Solution of Single-Multishape Sum Multipartition Problems with f Asymmetric Schur Convex by Optimization Over the Multipartition Polytope -- 5.6 Sum Multipartition Problems: Explicit Solutions -- 6. Applications -- 6.1 Assembly of Systems -- 6.2 Group Testing -- 6.3 Circuit Card Library -- 6.4 Clustering -- 6.5 Abstraction of Finite State Machines -- 6.6 Multischeduling -- 6.7 Cache Assignment -- 6.8 The Blood Analyzer Problem -- 6.9 Joint Replenishment of Inventory -- 6.10 Statistical Hypothesis Testing -- 6.11 Nearest Neighbor Assignment -- 6.12 Graph Partitions -- 6.13 The Traveling Salesman Problem -- 6.14 Vehicle Routing -- 6.15 Division of Property -- 6.16 The Consolidation of Farmland -- Bibliography -- Index.