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Extensions of Dynamic Programming for Combinatorial Optimization and Data Mining

  • Hassan AbouEisha
  • Talha Amin
  • Igor Chikalov
  • Shahid Hussain
  • Mikhail Moshkov

Part of the Intelligent Systems Reference Library book series (ISRL, volume 146)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Hassan AbouEisha, Talha Amin, Igor Chikalov, Shahid Hussain, Mikhail Moshkov
    Pages 1-12
  3. Common Tools: Pareto Optimal Points and Decision Tables

    1. Front Matter
      Pages 13-13
    2. Hassan AbouEisha, Talha Amin, Igor Chikalov, Shahid Hussain, Mikhail Moshkov
      Pages 15-21
    3. Hassan AbouEisha, Talha Amin, Igor Chikalov, Shahid Hussain, Mikhail Moshkov
      Pages 23-31
  4. Decision Trees

    1. Front Matter
      Pages 33-33
    2. Hassan AbouEisha, Talha Amin, Igor Chikalov, Shahid Hussain, Mikhail Moshkov
      Pages 35-48
    3. Hassan AbouEisha, Talha Amin, Igor Chikalov, Shahid Hussain, Mikhail Moshkov
      Pages 49-71
    4. Hassan AbouEisha, Talha Amin, Igor Chikalov, Shahid Hussain, Mikhail Moshkov
      Pages 73-84
    5. Hassan AbouEisha, Talha Amin, Igor Chikalov, Shahid Hussain, Mikhail Moshkov
      Pages 85-104
    6. Hassan AbouEisha, Talha Amin, Igor Chikalov, Shahid Hussain, Mikhail Moshkov
      Pages 105-122
  5. Decision Rules and Systems of Decision Rules

    1. Front Matter
      Pages 123-123
    2. Hassan AbouEisha, Talha Amin, Igor Chikalov, Shahid Hussain, Mikhail Moshkov
      Pages 125-129
    3. Hassan AbouEisha, Talha Amin, Igor Chikalov, Shahid Hussain, Mikhail Moshkov
      Pages 131-149
    4. Hassan AbouEisha, Talha Amin, Igor Chikalov, Shahid Hussain, Mikhail Moshkov
      Pages 151-172
    5. Hassan AbouEisha, Talha Amin, Igor Chikalov, Shahid Hussain, Mikhail Moshkov
      Pages 173-188
  6. Element Partition Trees

    1. Front Matter
      Pages 189-189
    2. Hassan AbouEisha, Talha Amin, Igor Chikalov, Shahid Hussain, Mikhail Moshkov
      Pages 191-205
    3. Hassan AbouEisha, Talha Amin, Igor Chikalov, Shahid Hussain, Mikhail Moshkov
      Pages 207-223
    4. Hassan AbouEisha, Talha Amin, Igor Chikalov, Shahid Hussain, Mikhail Moshkov
      Pages 225-233
  7. Combinatorial Optimization Problems

    1. Front Matter
      Pages 235-235
    2. Hassan AbouEisha, Talha Amin, Igor Chikalov, Shahid Hussain, Mikhail Moshkov
      Pages 237-243
    3. Hassan AbouEisha, Talha Amin, Igor Chikalov, Shahid Hussain, Mikhail Moshkov
      Pages 245-252
    4. Hassan AbouEisha, Talha Amin, Igor Chikalov, Shahid Hussain, Mikhail Moshkov
      Pages 253-259
    5. Hassan AbouEisha, Talha Amin, Igor Chikalov, Shahid Hussain, Mikhail Moshkov
      Pages 261-268
  8. Back Matter
    Pages 269-280

About this book

Introduction

Dynamic programming is an efficient technique for solving optimization problems. It is based on breaking the initial problem down into simpler ones and solving these sub-problems, beginning with the simplest ones. A conventional dynamic programming algorithm returns an optimal object from a given set of objects. This book develops extensions of dynamic programming, enabling us to (i) describe the set of objects under consideration; (ii) perform a multi-stage optimization of objects relative to different criteria; (iii) count the number of optimal objects; (iv) find the set of Pareto optimal points for bi-criteria optimization problems; and (v) to study relationships between two criteria. It considers various applications, including optimization of decision trees and decision rule systems as algorithms for problem solving, as ways for knowledge representation, and as classifiers; optimization of element partition trees for rectangular meshes, which are used in finite element methods for solving PDEs; and multi-stage optimization for such classic combinatorial optimization problems as matrix chain multiplication, binary search trees, global sequence alignment, and shortest paths. The results presented are useful for researchers in combinatorial optimization, data mining, knowledge discovery, machine learning, and finite element methods, especially those working in rough set theory, test theory, logical analysis of data, and PDE solvers. This book can be used as the basis for graduate courses.

 


Keywords

Dynamic Programming Pareto Optimal Points Bi-criteria Optimization Problem Matrix Chain Multiplication Multi-pruning for Decision Trees Procedure of Optimization

Authors and affiliations

  • Hassan AbouEisha
    • 1
  • Talha Amin
    • 2
  • Igor Chikalov
    • 3
  • Shahid Hussain
    • 4
  • Mikhail Moshkov
    • 5
  1. 1.Computer, Electrical and Mathematical Sciences and Engineering DivisionKing Abdullah University of Science and TechnologyThuwalSaudi Arabia
  2. 2.Computer, Electrical and Mathematical Sciences and Engineering DivisionKing Abdullah University of Science and TechnologyThuwalSaudi Arabia
  3. 3.Computer, Electrical and Mathematical Sciences and Engineering DivisionKing Abdullah University of Science and TechnologyThuwalSaudi Arabia
  4. 4.Computer, Electrical and Mathematical Sciences and Engineering DivisionKing Abdullah University of Science and TechnologyThuwalSaudi Arabia
  5. 5.Computer, Electrical and Mathematical Sciences and Engineering DivisionKing Abdullah University of Science and TechnologyThuwalSaudi Arabia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-91839-6
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2019
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-91838-9
  • Online ISBN 978-3-319-91839-6
  • Series Print ISSN 1868-4394
  • Series Online ISSN 1868-4408
  • Buy this book on publisher's site