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Accelerating Local Search for the Maximum Independent Set Problem

  • Jakob Dahlum
  • Sebastian Lamm
  • Peter Sanders
  • Christian Schulz
  • Darren StrashEmail author
  • Renato F. Werneck
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9685)

Abstract

Computing high-quality independent sets quickly is an important problem in combinatorial optimization. Several recent algorithms have shown that kernelization techniques can be used to find exact maximum independent sets in medium-sized sparse graphs, as well as high-quality independent sets in huge sparse graphs that are intractable for exact (exponential-time) algorithms. However, a major drawback of these algorithms is that they require significant preprocessing overhead, and therefore cannot be used to find a high-quality independent set quickly.

In this paper, we show that performing simple kernelization techniques in an online fashion significantly boosts the performance of local search, and is much faster than pre-computing a kernel using advanced techniques. In addition, we show that cutting high-degree vertices can boost local search performance even further, especially on huge (sparse) complex networks. Our experiments show that we can drastically speed up the computation of large independent sets compared to other state-of-the-art algorithms, while also producing results that are very close to the best known solutions.

Keywords

Maximum independent set Minimum vertex cover Local search Kernelization Reduction 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Jakob Dahlum
    • 1
  • Sebastian Lamm
    • 1
  • Peter Sanders
    • 1
  • Christian Schulz
    • 1
  • Darren Strash
    • 1
    Email author
  • Renato F. Werneck
    • 2
  1. 1.Institute of Theoretical InformaticsKarlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.San FranciscoUSA

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