Balanced matrix

Abstract: Here is the story of how this paper was written. (a) Independently, Alan and Joe discovered this easy theorem: if the “right hand side” consists of integers, and if the matrix is “totally unimodular”, then the vertices of the polyhedron defined by the linear inequalities will all be integral. This is easy to prove and useful. As far as we know, this is the only part of our theorem that anyone has ever used.

Abstract: Preface 1. Clutters 2. T-Cuts and T-Joins 3. Perfect Graphs and Matrices 4. Ideal Matrices 5. Odd Cycles in Graphs 6. 0,+1 Matrices and Integral Polyhedra 7. Signing 0,1 Matrices to Be Totally Unimodular or Balanced 8. Decomposition by k-Sum 9. Decomposition of Balanced Matrices 10. Decomposition of Perfect Graphs Bibliography Index.

Abstract: A zero---one matrix is called perfect if the polytope of the associated set packing problem has integral vertices only. By this definition, all totally unimodular zero---one matrices are perfect. In this paper we give a characterization of perfect zero---one matrices in terms offorbidden submatrices. Perfect zero---one matrices are closely related to perfect graphs and constitute a generalization of balanced matrices as introduced by C. Berge. Furthermore, the results obtained here bear on an unsolved problem in graph theory, the strong perfect graph conjecture, also due to C. Berge.

Abstract: Preface. Introduction: Matrix Organizations: What Are They? Where Did They Come From? What Is a Matrix? What Are the Origins of the Matrix? What Happened? The Star Model. Implications of the Star Model. PART ONE: SIMPLE MATRIX ORGANIZATIONS. 1. Simple Matrix Structures. Two-Dimensional Structures. Pharmaceutical R&D Lab Example. Summary. 2. The Two-Hat Model. What Is the Two-Hat Model? Examples of Two-Hat Structures. Summary. 3. The Baton Pass Model. The Consumer Goods Model. The Pharmaceutical Model. Summary. 4. The Matrix Within a Matrix. Design Challenges of the Matrix Within a Matrix. Matrix Within a Matrix at the Corporate Level. Mars Pet Food Example. Summary. 5. Balancing Power and Defining Roles. Designing Power Bases. Roles and Responsibilities. Summary. PART TWO: COMPLEX MATRIX STRUCTURES. 6. The Three-Dimensional Matrix. International Strategy. The Geography-Dominant Matrix. The Balanced Matrix. The Business-Dominant Matrix. Differentiated Structures. Other Three-Dimensional Models. Summary. 7. More Complex Matrix Structures. Global Account Teams. The Front-Back Hybrid Model. Summary. 8. The IBM Structure. The IBM Front-Back Hybrid. More Complexity? Summary. PART THREE: COMPLETING THE STAR MODEL. 9. Communication in the Matrix. Informal Communication. Formal Communication. Summary. 10. Planning and Coordination Processes. Goal Alignment, Dispute Resolution, and Coordination Mechanisms. Summary. 11. Planning Processes in the Complex Matrix. What About Complex Matrix Designs? Get the System in a Room. Online Processes. Summary. 12. Human Resources Policies. Human Capital. Social Capital. Summary. 13. Leadership in a Matrix Organization. Seeing That Conflicts Are Resolved. Managing the Top Team. Balancing Power. Summary. 14. Implementing a Matrix. Using the Star Model. Building Capabilities. Summary. 15. A Synopsis of Matrix Capabilities. Epilogue: Personal Stories: The Use and Abuse of the Matrix. Early Phase: "What Is a Matrix, Anyway"? Matrix Takes Off and Becomes Trendy. The Phase of Decline. The Stealth Matrix Phase. Today: Matrix out of the Closet. References. About the Author. Index.