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1-Complex s, t Hamiltonian Paths: Structure and Reconfiguration in Rectangular Grids

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WALCOM: Algorithms and Computation (WALCOM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13174))

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Abstract

We give a complete structure theorem for 1-complex s, t Hamiltonian paths in rectangular grid graphs. We use the structure theorem to design an algorithm to reconfigure one such path into any other in linear time, making a linear number of switch operations in grid cells.

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References

  1. Collins, K.L., Krompart, L.B.: The number of Hamiltonian paths in a rectangular grid. Discrete Math. 169(1–3), 29–38 (1997)

    Article  MathSciNet  Google Scholar 

  2. Everett, H.: Hamiltonian paths in nonrectangular grid graphs. Master’s thesis, University of Saskatchewan, Canada (1986)

    Google Scholar 

  3. Fellows, M., et al.: Milling a graph with turn costs: a parameterized complexity perspective. In: Thilikos, D.M. (ed.) WG 2010. LNCS, vol. 6410, pp. 123–134. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-16926-7_13

    Chapter  Google Scholar 

  4. Gorbenko, A., Popov, V., Sheka, A.: Localization on discrete grid graphs. In: He, X., Hua, E., Lin, Y., Liu, X. (eds.) Computer, Informatics, Cybernetics and Applications. LNEE, vol. 107, pp. 971–978. Springer, Dordrecht (2012). https://doi.org/10.1007/978-94-007-1839-5_105

  5. Itai, A., Papadimitriou, C.H., Szwarcfiter, J.L.: Hamilton paths in grid graphs. SIAM J. Comput. 11(4), 676–686 (1982)

    Article  MathSciNet  Google Scholar 

  6. Jacobsen, J.L.: Exact enumeration of Hamiltonian circuits, walks and chains in two and three dimensions. J. Phys. A Math. Theor. 40, 14667–14678 (2007)

    Article  MathSciNet  Google Scholar 

  7. Keshavarz-Kohjerdi, F., Bagheri, A.: Hamiltonian paths in L-shaped grid graphs. Theor. Comput. Sci. 621, 37–56 (2016)

    Article  MathSciNet  Google Scholar 

  8. Muller, P., Hascoet, J.Y., Mognol, P.: Toolpaths for additive manufacturing of functionally graded materials (FGM) parts. Rapid Prototyp. J. 20(6), 511–522 (2014)

    Article  Google Scholar 

  9. Nishat, R.I., Srinivasan, V., Whitesides, S.: Reconfiguring simple s, t Hamiltonian paths in rectangular grid graphs. In: Flocchini, P., Moura, L. (eds.) IWOCA 2021. LNCS, vol. 12757, pp. 501–515. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-79987-8_35

    Chapter  Google Scholar 

  10. Nishat, R.I., Whitesides, S.: Reconfiguring Hamiltonian cycles in L-shaped grid graphs. In: Sau, I., Thilikos, D.M. (eds.) WG 2019. LNCS, vol. 11789, pp. 325–337. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-30786-8_25

    Chapter  MATH  Google Scholar 

  11. Nishat, R.I., Whitesides, S.: Bend complexity and Hamiltonian cycles in grid graphs. In: Cao, Y., Chen, J. (eds.) COCOON 2017. LNCS, vol. 10392, pp. 445–456. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-62389-4_37

    Chapter  MATH  Google Scholar 

  12. Bodroz̃a Pantić, O., Pantić, B., Pantić, I., Bodroz̃a Solarov, M.: Enumeration of Hamiltonian cycles in some grid graphs. MATCH Commun. Math. Comput. Chem. 70, 181–204 (2013)

    Google Scholar 

  13. Takaoka, A.: Complexity of Hamiltonian cycle reconfiguration. Algorithms 11(9), 140 (2018)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Ryerson University, Toronto, ON, Canada

    Rahnuma Islam Nishat

  2. Department of Computer Science, University of Victoria, Victoria, BC, Canada

    Venkatesh Srinivasan & Sue Whitesides

Authors
  1. Rahnuma Islam Nishat
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  2. Venkatesh Srinivasan
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  3. Sue Whitesides
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Corresponding author

Correspondence to Rahnuma Islam Nishat .

Editor information

Editors and Affiliations

  1. University of Bonn, Bonn, Germany

    Petra Mutzel

  2. Bangladesh University of Engineering and Technology (BUET), Dhaka, Bangladesh

    Md. Saidur Rahman

  3. Universitas Jember, Jember, Indonesia

    Slamin

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Nishat, R.I., Srinivasan, V., Whitesides, S. (2022). 1-Complex s, t Hamiltonian Paths: Structure and Reconfiguration in Rectangular Grids. In: Mutzel, P., Rahman, M.S., Slamin (eds) WALCOM: Algorithms and Computation. WALCOM 2022. Lecture Notes in Computer Science(), vol 13174. Springer, Cham. https://doi.org/10.1007/978-3-030-96731-4_6

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  • DOI: https://doi.org/10.1007/978-3-030-96731-4_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-96730-7

  • Online ISBN: 978-3-030-96731-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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