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Linear Programming

In: Design and Analysis of Approximation Algorithms

Author

Listed:
  • Ding-Zhu Du

    (University of Texas at Dallas)

  • Ker-I Ko

    (State University of New York at Stony Brook)

  • Xiaodong Hu

    (Academy of Mathematics and Systems Science Chinese Academy of Sciences)

Abstract

A widely used relaxation technique for approximation algorithms is to convert an optimization problem into an integer linear program and then relax the constraints on the solutions allowing them to assume real, noninteger values. As the optimal solution to a (real-valued) linear program can be found in polynomial time, we can then solve the linear program and round the solutions to integers as the solutions for the original problem. In this chapter, we give a brief introduction to the theory of linear programming and discuss various rounding techniques.

Suggested Citation

  • Ding-Zhu Du & Ker-I Ko & Xiaodong Hu, 2012. "Linear Programming," Springer Optimization and Its Applications, in: Design and Analysis of Approximation Algorithms, chapter 7, pages 245-296, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-1701-9_7
    DOI: 10.1007/978-1-4614-1701-9_7
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