Skip to main content
SpringerLink
Log in
Book cover

Encyclopedia of Algorithms pp 1728–1732Cite as

Random Planted 3-SAT

  • Reference work entry
  • First Online:

  • 45 Accesses

Years and Authors of Summarized Original Work

  • 2003; Flaxman

Problem Definition

This classic problem in complexity theory is concerned with efficiently finding a satisfying assignment to a propositional formula. The input is a formula with n Boolean variables which is expressed as an AND of ORs with 3 variables in each OR clause (a 3-CNF formula). The goal is to (1) find an assignment of variables to TRUE and FALSE so that the formula has value TRUE or (2) prove that no such assignment exists. Historically, recognizing satisfiable 3-CNF formulas was the first “natural” example of an NP-complete problem, and, because it is NP-complete, no polynomial-time algorithm can succeed on all 3-CNF formulas unless P = NP [4, 10]. Because of the numerous practical applications of 3-SAT, and also due to its position as the canonical NP-complete problem, many heuristic algorithms have been developed for solving3-SAT, and some of these algorithms have been analyzed rigorously on random instances.

Notation...

This is a preview of subscription content, 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

Learn about institutional subscriptions

Recommended Reading

  1. Alon N, Kahale N (1997) A spectral technique for coloring random 3-colorable graphs. SIAM J Comput 26(6):1733–1748

    Article  MathSciNet  MATH  Google Scholar 

  2. Barthel W, Hartmann AK, Leone M, Ricci-Tersenghi F, Weigt M, Zecchina R (2002) Hiding solutions in random satisfiability problems: a statistical mechanics approach. Phys Rev Lett 88:188701

    Article  Google Scholar 

  3. Chen H, Frieze AM (1996) Coloring bipartite hypergraphs. In: Cunningham HC, McCormick ST, Queyranne M (eds) Integer programming and combinatorial optimization, 5th international IPCO conference, Vancouver, 3–5 June 1996. Lecture notes in computer science, vol 1084. Springer, pp 345–358

    Google Scholar 

  4. Cook S (1971) The complexity of theorem-proving procedures. In: Proceedings of the 3rd annual symposium on theory of computing, Shaker Heights, 3–5 May, pp 151–158

    Google Scholar 

  5. Feige U, Mossel E, Vilenchik D (2006) Complete convergence of message passing algorithms for some satisfiability problems. In: Díaz J, Jansen K, Rolim JDP, Zwick U (eds) Approximation, randomization, and combinatorial optimization. Algorithms and techniques, 9th international workshop on approximation algorithms for combinatorial optimization problems, APPROX 2006 and 10th International Workshop on Randomization and Computation, RANDOM 2006, Barcelona, 28–30 Aug 2006. Lecture notes in computer science, vol 4110. Springer, pp 339–350

    Google Scholar 

  6. Feige U, Vilenchik D (2004) A local search algorithm for 3-SAT. Technical report, The Weizmann Institute, Rehovat

    Google Scholar 

  7. Flaxman AD (2003) A spectral technique for random satisfiable 3CNF formulas. In: Proceedings of the fourteenth annual ACM-SIAM symposium on discrete algorithms, Baltimore. ACM, New York, pp 357–363

    Google Scholar 

  8. Koutsoupias E, Papadimitriou CH (1992) On the greedy algorithm for satisfiability. Inf Process Lett 43(1):53–55

    Article  MathSciNet  MATH  Google Scholar 

  9. Krivelevich M, Vilenchik D (2006) Solving random satisfiable 3CNF formulas in expected polynomial time. In: Proceedings of the 17th annual ACM-SIAM symposium on discrete algorithm (SODA ’06), Miami. ACM

    Google Scholar 

  10. Levin LA (1973) Universal enumeration problems. Probl Pereda Inf 9(3):115–116

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Theory Group, Microsoft Research, Redmond, WA, USA

    Abraham Flaxman

Authors
  1. Abraham Flaxman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abraham Flaxman .

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

Flaxman, A. (2016). Random Planted 3-SAT. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_330

Download citation

Publish with us

Policies and ethics

Search

Navigation