Partitions: Optimality And Clustering: Vol II: Multi-Parameter, 1st Edition

  • Volume 2
  • Published By: World Scientific Publishing Company
  • ISBN-10: 981441235X
  • ISBN-13: 9789814412353
  • DDC: 512.7
  • Grade Level Range: College Freshman - College Senior
  • 304 Pages | eBook
  • Original Copyright 2013 | Published/Released January 2015
  • This publication's content originally published in print form: 2013

  • Price:  Sign in for price



The 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 problems of optimal partitions are dealt with. The authors show how they can be solved using the theory - or why they cannot be. These problems include: allocation of components to maximize system reliability; experiment design to identify defectives; design of circuit card library and of blood analyzer lines; abstraction of finite state machines and assignment of cache items to pages; the division of property and partition bargaining as well as touching on those well-known research areas such as scheduling, inventory, nearest neighbor assignment, the traveling salesman problem, vehicle routing, and graph partitions. The authors elucidate why the last three problems cannot be solved in the context of the theory.

Table of Contents

Front Cover.
Half Title Page.
Other Front Matter.
Title Page.
Copyright Page.
1: Bounded-Shape Sum-Partition Problems: Polyhedral Approach.
2: Constrained-Shape and Single-Size Sum-Partition Problems: Polynomial Approach.
3: Partitions Over Multi-Parameter Spaces: Combinatorial Structure.
4: Clustering Problems Over Multi-Parameter Spaces.
5: Sum-Multipartition Problems Over Single-Parameter Spaces.
6: Applications.