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Kernelization – Preprocessing with a Guarantee

  • Daniel Lokshtanov
  • Neeldhara Misra
  • Saket Saurabh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7370)

Abstract

Data reduction techniques are widely applied to deal with computationally hard problems in real world applications. It has been a long-standing challenge to formally express the efficiency and accuracy of these “pre-processing” procedures. The framework of parameterized complexity turns out to be particularly suitable for a mathematical analysis of pre-processing heuristics. A kernelization algorithm is a pre-processing algorithm which simplifies the instances given as input in polynomial time, and the extent of simplification desired is quantified with the help of the additional parameter.

We give an overview of some of the early work in the area and also survey newer techniques that have emerged in the design and analysis of kernelization algorithms. We also outline the framework of Bodlaender et al. [9] and Fortnow and Santhanam [38] for showing kernelization lower bounds under reasonable assumptions from classical complexity theory, and highlight some of the recent results that strengthen and generalize this framework.

Keywords

Planar Graph Vertex Cover Parameterized Problem Polynomial Kernel Truth Assignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Daniel Lokshtanov
    • 1
  • Neeldhara Misra
    • 2
  • Saket Saurabh
    • 2
  1. 1.University of CaliforniaSan DiegoUSA
  2. 2.The Institute of Mathematical SciencesChennaiIndia

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