Skip to main content
SpringerLink
Log in

Exact Algorithms and Strong Exponential Time Hypothesis

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

Years and Authors of Summarized Original Work

  • 2010; PăatraÅŸscu, Williams

  • 2011; Lokshtanov, Marx, Saurabh

  • 2012; Cygan, Dell, Lokshtanov, Marx, Nederlof, Okamoto, Paturi, Saurabh, Wahlström

Problem Definition

All problems in NP can be exactly solved in 2poly(n) time via exhaustive search, but research has yielded faster exponential-time algorithms for many NP-hard problems. However, some key problems have not seen improved algorithms, and problems with improvements seem to converge toward O(Cn) for some unknown constant C > 1.

The satisfiability problem for Boolean formulas in conjunctive normal form, CNF-SAT, is a central problem that has resisted significant improvements. The complexity of CNF-SAT and its special case k-SAT, where each clause has k literals, is the canonical starting point for the development of NP-completeness theory.

Similarly, in the last 20 years, two hypotheses have emerged as powerful starting points for understanding exponential-time complexity. In 1999,...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 1,599.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 1,999.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Recommended Reading

  1. Calabro C, Impagliazzo R, Paturi R (2009) The complexity of satisfiability of small depth circuits. In: Chen J, Fomin F (eds) Parameterized and exact computation. Lecture notes in computer science, vol 5917. Springer, Berlin/Heidelberg, pp 75–85. doi:10.1007/978-3-642-11269-0_6. http://dx.doi.org/10.1007/978-3-642-11269-0_6

  2. Chen J, Chor B, Fellows M, Huang X, Juedes D, Kanj IA, Xia G (2005) Tight lower bounds for certain parameterized np-hard problems. Inf Comput 201(2):216–231. doi:http://dx.doi.org/10.1016/j.ic.2005.05.001. http://www.sciencedirect.com/science/article/pii/S0890540105000763

  3. Cygan M, Dell H, Lokshtanov D, Marx D, Nederlof J, Okamoto Y, Paturi R, Saurabh S, Wahlstrom M (2012) On problems as hard as cnf-sat. In: Proceedings of the 2012 IEEE conference on computational complexity (CCC ’12), Washington, DC. IEEE Computer Society, pp 74–84. doi:10.1109/CCC.2012.36. http://dx.doi.org/10.1109/CCC.2012.36

  4. Fomin F, Kratsch D (2010) Exact exponential algorithms. Texts in theoretical computer science, an EATCS series. Springer, Berlin/Heidelberg

    Google Scholar 

  5. Impagliazzo R, Paturi R (2001) On the complexity of k-sat. J Comput Syst Sci 62(2):367–375. doi:http://dx.doi.org/10.1006/jcss.2000.1727. http://www.sciencedirect.com/science/article/pii/S0022000000917276

  6. Impagliazzo R, Paturi R, Zane F (2001) Which problems have strongly exponential complexity? J Comput Syst Sci 63(4):512–530. doi:http://dx.doi.org/10.1006/jcss.2001.1774. http://www.sciencedirect.com/science/article/pii/S002200000191774X

  7. Lokshtanov D, Marx D, Saurabh S (2011) Known algorithms on graphs of bounded treewidth are probably optimal. In: Proceedings of the twenty-second Annual ACM-SIAM symposium on discrete algorithms (SODA ’11), San Francisco. SIAM, pp 777–789. http://dl.acm.org/citation.cfm?id=2133036.2133097

    Chapter  Google Scholar 

  8. Pătraşcu M, Williams R (2010) On the possibility of faster sat algorithms. In: Proceedings of the twenty-first annual ACM-SIAM symposium on discrete algorithms (SODA ’10), Philadelphia. Society for Industrial and Applied Mathematics, pp 1065–1075. http://dl.acm.org/citation.cfm?id=1873601.1873687

    Chapter  Google Scholar 

  9. Woeginger G (2003) Exact algorithms for np-hard problems: a survey. In: Jünger M, Reinelt G, Rinaldi G (eds) Combinatorial optimization Eureka, you shrink! Lecture notes in computer science, vol 2570. Springer, Berlin/Heidelberg, pp 185–207. doi:10.1007/3-540-36478-1_17. http://dx.doi.org/10.1007/3-540-36478-1_17

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Stanford University, Stanford, CA, USA

    Joshua R. Wang

  2. Department of Computer Science, Stanford University, Stanford, CA, USA

    Ryan Williams

Authors
  1. Joshua R. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ryan Williams
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joshua R. Wang .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media New York

About this entry

Cite this entry

Wang, J.R., Williams, R. (2016). Exact Algorithms and Strong Exponential Time Hypothesis. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_519

Download citation

Publish with us

Policies and ethics

Search

Navigation