Nothing Special   »   [go: up one dir, main page]

Skip to main content

A SAT Based Effective Algorithm for the Directed Hamiltonian Cycle Problem

  • Conference paper
Computer Science – Theory and Applications (CSR 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6072))

Included in the following conference series:

  • 751 Accesses

Abstract

The Hamiltonian cycle problem (HCP) is an important combinatorial problem with applications in many areas. While thorough theoretical and experimental analyses have been made on the HCP in undirected graphs, little is known for the HCP in directed graphs (DHCP). The contribution of this work is an effective algorithm for the DHCP. Our algorithm explores and exploits the close relationship between the DHCP and the Assignment Problem (AP) and utilizes a technique based on Boolean satisfiability (SAT). By combining effective algorithms for the AP and SAT, our algorithm significantly outperforms previous exact DHCP algorithms including an algorithm based on the award-winning Concorde TSP algorithm.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Angluin, D., Valiant, L.G.: Fast Probabilistic Algorithms for Hamiltonian Circuits and Matchings. J. Comput. System. Sci. 18(2), 155–193 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  2. Applegate, D.L., Bixby, R.E., Chvátal, V., Cook, W.J.: The Traveling Salesman Problem. A Computational Study. Princeton University Press, Princeton (2006)

    MATH  Google Scholar 

  3. Bang-Jensen, J., Gutin, G.: Digraphs: Theory, Algorithms and Applications, ch. 5. Springer, London (2008), http://www.cs.rhul.ac.uk/books/dbook/

    Google Scholar 

  4. Bollobás, B., Fenner, T.I., Frieze, A.M.: An Algorithm for Finding Hamiltonian Paths and Cycles in Random Graphs. Combinatorica 7(4), 327–341 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  5. Christofides, N.: Graph Theory – An Algorithmic Approach. Academic Press, New York (1975)

    MATH  Google Scholar 

  6. Chvátal, V.: Hamiltonian Cycles. In: Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B. (eds.) The Traveling Salesman Problem. A Guided Tour of Combinatorial Optimization, ch. 11. John Wiley & Sons, Chichester (1985)

    Google Scholar 

  7. Eén, N., Sörensson, N.: An Extensible SAT-Solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)

    Google Scholar 

  8. Frieze, A.M.: Finding Hamiltonian Cycles in Sparse Random Graphs. J. Combin. Theory Ser. B 44, 230–250 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  9. Frieze, A.M.: An Algorithm for Finding Hamilton Cycles in Random Directed Graphs. J. Algorithms 9, 181–204 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  10. Frieze, A.M., Suen, S.: Counting Hamilton cycles in random directed graphs. Random Structures Algorithms 9, 235–242 (1992)

    Article  MathSciNet  Google Scholar 

  11. Glover, F., Gutin, G., Yeo, A., Zverovich, A.: Construction Heuristics for the Asymmetric TSP. European J. Oper. Res. 129, 555–568 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. Goldengorin, B., Jäger, G., Molitor, P.: Tolerance Based Contract-or-Patch Heuristic for the Asymmetric TSP. In: Erlebach, T. (ed.) CAAN 2006. LNCS, vol. 4235, pp. 86–97. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  13. Gould, R.J.: Updating the Hamiltonian Problem – a Survey. J. Graph Theory 15(2), 121–157 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  14. Grebinski, V., Kucherov, G.: Reconstructing a Hamiltonian Circuit by Querying the Graph: Application to DNA Physical Mapping. IR 96-R-123, Centre de Recherche en Informatique de Nancy (1996)

    Google Scholar 

  15. Henderson, R., Apodaca, E.: A Knight of Egodeth: Zen Raptured Quietude. Book Surge Publishing (2008)

    Google Scholar 

  16. Jin, H., Han, H., Somenzi, F.: Efficient Conflict Analysis for Finding All Satisfying Assignments of a Boolean Circuit. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 287–300. Springer, Heidelberg (2005)

    Google Scholar 

  17. Johnson, D.S., Gutin, G., McGeoch, L.A., Yeo, A., Zhang, W., Zverovich, A.: Experimental Analysis of Heuristics for the ATSP. In: Gutin, G., Punnen, A.P. (eds.) The Traveling Salesman Problem and Its Variations, ch. 10. Kluwer, Dordrecht (2002)

    Google Scholar 

  18. Jonker, R., Volgenant, A.: Transforming Asymmetric into Symmetric Traveling Salesman Problems. Oper. Res. Lett. 2(4), 161–163 (1983)

    Article  MATH  Google Scholar 

  19. Jonker, R., Volgenant, A.: A Shortest Augmenting Path Algorithm for Dense and Sparse Linear Assignment Problems. Computing 38, 325–340 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  20. Karp, R.M.: Reducibility Among Combinatorial Problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum, New York (1972)

    Google Scholar 

  21. Karp, R.M., Steele, J.M.: Probabilistic Analysis of Heuristics. In: Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B. (eds.) The Traveling Salesman Problem. A Guided Tour of Combinatorial Optimization, ch. 6. John Wiley & Sons, Chicester (1985)

    Google Scholar 

  22. Kelly, L.: Hamilton Cycles in Directed Graphs. PhD Thesis, University of Birmingham, United Kingdom (2007)

    Google Scholar 

  23. Komlós, M., Szemerédi, E.: Limit Distribution for the Existence of a Hamiltonian Cycle in a Random Graph. Discrete Math. 43, 55–63 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  24. Kyek, O., Parberry, I., Wegener, I.: Bounds on the Number of Knight’s Tours. Discrete Appl. Math. 74(2), 171–181 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  25. Lynce, I., Marques-Silva, J.: Efficient Haplotype Inference with Boolean Satisfiability. In: Proc. 21st National Conference on Artificial Intelligence (AAAI). AAAI Press, Menlo Park (2006)

    Google Scholar 

  26. Martello, S.: An Enumerative Algorithm for Finding Hamiltonian Circuits in a Directed Graph. ACM Trans. Math. Software 9(1), 131–138 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  27. McDiarmid, C.J.H.: Cluster Percolation and Random Graphs. Math. Program. Stud. 13, 17–25 (1980)

    MATH  MathSciNet  Google Scholar 

  28. Pósa, L.: Hamiltonian Circuits in Random Graphs. Discrete Math. 14, 359–364 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  29. Stojaković, M., Szabó, T.: Positional Games on Random Graphs. Random Structures Algorithms 26(1-2), 204–223 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  30. Vandegriend, B.: Finding Hamiltonian Cycles: Algorithms, Graphs and Performance. Master Thesis, University of Alberta, Canada (1998)

    Google Scholar 

  31. 8th DIMACS Implementation Challenge: The Traveling Salesman Problem, http://www.research.att.com/~dsj/chtsp/

  32. The Hamiltonian Page by Gutin, G., Moscato, P.: http://www.ing.unlp.edu.ar/cetad/mos/Hamilton.html

  33. The Stony Brook Algorithm Repository by Skiena, S.: http://www.cs.sunysb.edu/~algorith/files/hamiltonian-cycle.shtml

  34. Source code of [2](Concorde), http://www.tsp.gatech.edu/concorde.html

  35. Source code of [7] (MiniSat), http://minisat.se

  36. Source code of [19], http://www.magiclogic.com/assignment.html

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jäger, G., Zhang, W. (2010). A SAT Based Effective Algorithm for the Directed Hamiltonian Cycle Problem. In: Ablayev, F., Mayr, E.W. (eds) Computer Science – Theory and Applications. CSR 2010. Lecture Notes in Computer Science, vol 6072. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13182-0_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-13182-0_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13181-3

  • Online ISBN: 978-3-642-13182-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics