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Invitation to Combinatorial Reconfiguration

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WALCOM: Algorithms and Computation (WALCOM 2022)

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Abstract

Combinatorial reconfiguration arises when we wish to find a step-by-step transformation on the solution space formed by feasible solutions of an instance of a search problem. Many reconfiguration problems have been shown PSPACE-complete, while several algorithmic techniques have been developed. In this talk, I will give a broad introduction of combinatorial reconfiguration.

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References

  1. Archer, A.F.: A modern treatment of the 15 puzzle. Am. Math. Mon. 106(9), 793–799 (1999)

    Article  MathSciNet  Google Scholar 

  2. Belmonte, R., Hanaka, T., Lampis, M., Ono, H., Otachi, Y.: Independent set reconfiguration parameterized by modular-width. Algorithmica 82(9), 2586–2605 (2020)

    Article  MathSciNet  Google Scholar 

  3. Belmonte, R., Kim, E.J., Lampis, M., Mitsou, V., Otachi, Y., Sikora, F.: Token sliding on split graphs. Theory Comput. Syst. 65(4), 662–686 (2021)

    Article  MathSciNet  Google Scholar 

  4. Bonamy, M., Bousquet, N.: Token sliding on chordal graphs. In: Bodlaender, H.L., Woeginger, G.J. (eds.) WG 2017. LNCS, vol. 10520, pp. 127–139. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-68705-6_10

    Chapter  Google Scholar 

  5. Bonsma, P.: Independent set reconfiguration in cographs and their generalizations. J. Graph Theory 83(2), 164–195 (2016)

    Article  MathSciNet  Google Scholar 

  6. Brewster, R.C., McGuinness, S., Moore, B., Noel, J.A.: A dichotomy theorem for circular colouring reconfiguration. Theoret. Comput. Sci. 639, 1–13 (2016)

    Article  MathSciNet  Google Scholar 

  7. Briański, M., Felsner, S., Hodor, J., Micek, P.: Reconfiguring independent sets on interval graphs. In: Bonchi, F., Puglisi, S.J. (eds.) 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics, Dagstuhl, Germany, vol. 202, pp. 23:1–23:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

    Google Scholar 

  8. Demaine, E.D., Rudoy, M.: A simple proof that the \((n^2-1)\)-puzzle is hard. Theoret. Comput. Sci. 732, 80–84 (2018)

    Article  MathSciNet  Google Scholar 

  9. Hearn, R.A., Demaine, E.D.: PSPACE-completeness of sliding-block puzzles and other problems through the nondeterministic constraint logic model of computation. Theoret. Comput. Sci. 343(1–2), 72–96 (2005)

    Article  MathSciNet  Google Scholar 

  10. Hearn, R.A., Demaine, E.D.: Games, Puzzles, and Computation. A. K. Peters Ltd, Natick (2009)

    Book  Google Scholar 

  11. van den Heuvel, J.: The complexity of change. In: Blackburn, S.R., Gerke, S., Wildon, M. (eds.) Surveys in Combinatorics 2013. London Mathematical Society Lecture Note Series, vol. 409, pp. 127–160. Cambridge University Press, Cambridge (2013)

    Chapter  Google Scholar 

  12. Hoang, D.A., Uehara, R.: Sliding tokens on a cactus. In: Hong, S.-H. (ed.) 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics, Dagstuhl, Germany, vol. 64, pp. 37:1–37:26. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2016)

    Google Scholar 

  13. Inoue, T., et al.: Distribution loss minimization with guaranteed error bound. IEEE Trans. Smart Grid 5(1), 102–111 (2014)

    Article  Google Scholar 

  14. Ito, T., et al.: On the complexity of reconfiguration problems. Theoret. Comput. Sci. 412(12–14), 1054–1065 (2011)

    Article  MathSciNet  Google Scholar 

  15. Kamiński, M., Medvedev, P., Milanič, M.: Complexity of independent set reconfigurability problems. Theoret. Comput. Sci. 439, 9–15 (2012)

    Article  MathSciNet  Google Scholar 

  16. Lokshtanov, D., Mouawad, A.E.: The complexity of independent set reconfiguration on bipartite graphs. ACM Trans. Algorithms 15(1), 7:1-7:19 (2019)

    Article  MathSciNet  Google Scholar 

  17. Mouawad, A.E., Nishimura, N., Raman, V., Siebertz, S.: Vertex cover reconfiguration and beyond. Algorithms 11(2), Paper ID 20 (2018)

    Google Scholar 

  18. Nishimura, N.: Introduction to reconfiguration. Algorithms 11(4), Paper ID 52 (2018)

    Google Scholar 

  19. Ratner, D., Warmuth, M.: The \((n^2-1)\)-puzzle and related relocation problems. J. Symb. Comput. 10(2), 111–137 (1990)

    Article  Google Scholar 

  20. Wrochna, M.: Reconfiguration in bounded bandwidth and tree-depth. J. Comput. Syst. Sci. 93, 1–10 (2018)

    Article  MathSciNet  Google Scholar 

  21. van der Zanden, T.C.: Parameterized complexity of graph constraint logic. In: Husfeldt, T., Kanj, I. (eds.) 10th International Symposium on Parameterized and Exact Computation (IPEC 2015). Leibniz International Proceedings in Informatics, Dagstuhl, Germany, vol. 43, pp. 282–293. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2015)

    Google Scholar 

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Acknowledgments

The author thanks Ryuhei Uehara and Yota Otachi for their helpful suggestions. This work is partially supported by JSPS KAKENHI Grant Numbers JP18H04091, JP19K11814 and JP20H05793, Japan.

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Authors and Affiliations

  1. Graduate School of Information Sciences, Tohoku University, Sendai, Japan

    Takehiro Ito

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  1. Takehiro Ito
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Correspondence to Takehiro Ito .

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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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Ito, T. (2022). Invitation to Combinatorial Reconfiguration. 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_3

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  • DOI: https://doi.org/10.1007/978-3-030-96731-4_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-96730-7

  • Online ISBN: 978-3-030-96731-4

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