Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

Lower Bounds Based on the Exponential Time Hypothesis: Edge Clique Cover

  • Michał PilipczukEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_777

Years and Authors of Summarized Original Work

  • 2008; Gramm, Guo, Hüffner, Niedermeier

  • 2013; Cygan, Pilipczuk, Pilipczuk

The Exponential Time Hypothesis and Its Consequences

In 2001, Impagliazzo, Paturi, and Zane [5, 6] introduced the Exponential Time Hypothesis (ETH): a complexity assumption saying that there exists a constant c > 0 such that no algorithm for 3-SATcan achieve the running time of \(\mathcal{O}(2^{cn})\)

Keywords

Cocktail party graph Edge clique cover Exponential Time Hypothesis Parameterized complexity 
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Recommended Reading

  1. 1.
    Cygan M, Pilipczuk M, Pilipczuk M (2013) Known algorithms for edge clique cover are probably optimal. In: Proceedings of the twenty-fourth annual ACM-SIAM symposium on discrete algorithms, SODA 2013, New Orleans, 6–8 Jan 2013, pp 1044–1053Google Scholar
  2. 2.
    Cygan M, Kratsch S, Pilipczuk M, Pilipczuk M, Wahlström M (2014) Clique cover and graph separation: new incompressibility results. TOCT 6(2):6MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Gramm J, Guo J, Hüffner F, Niedermeier R (2008) Data reduction and exact algorithms for clique cover. ACM J Exp Algorithmics 13:article 2.2Google Scholar
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    Gregory DA, Pullman NJ (1982) On a clique covering problem of Orlin. Discret Math 41(1): 97–99MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Impagliazzo R, Paturi R (2001) On the complexity of k-SAT. J Comput Syst Sci 62(2):367–375MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Impagliazzo R, Paturi R, Zane F (2001) Which problems have strongly exponential complexity? J Comput Syst Sci 63(4):512–530MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Lokshtanov D, Marx D, Saurabh S (2011) Lower bounds based on the exponential time hypothesis. Bull EATCS 105:41–72MathSciNetzbMATHGoogle Scholar
  8. 8.
    Lokshtanov D, Marx D, Saurabh S (2011) Slightly superexponential parameterized problems. In: Proceedings of the twenty-second annual ACM-SIAM symposium on discrete algorithms, SODA 2011, San Francisco, 23–25 Jan 2011. SIAM, pp 760–776Google Scholar
  9. 9.
    Pilipczuk M (2013) Tournaments and optimality: new results in parameterized complexity. PhD thesis, University of Bergen, Norway. Available at the webpage of the authorGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Institute of InformaticsUniversity of WarsawWarsawPoland
  2. 2.Institute of InformaticsUniversity of BergenBergenNorway