On the Complexity of Reconfiguration Problems

  • Takehiro Ito
  • Erik D. Demaine
  • Nicholas J. A. Harvey
  • Christos H. Papadimitriou
  • Martha Sideri
  • Ryuhei Uehara
  • Yushi Uno
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5369)


Reconfiguration problems arise when we wish to find a step-by-step transformation between two feasible solutions of a problem such that all intermediate results are also feasible. We demonstrate that a host of reconfiguration problems derived from NP-complete problems are PSPACE-complete, while some are also NP-hard to approximate. In contrast, several reconfiguration versions of problems in P are solvable in polynomial time.


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  1. 1.
    Bonsma, P., Cereceda, L.: Finding paths between graph colourings: PSPACE-completeness and superpolynomial distances. In: Kučera, L., Kučera, A. (eds.) MFCS 2007. LNCS, vol. 4708, pp. 738–749. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  2. 2.
    Cook, W.J., Cunningham, W.H., Pulleyblank, W.R., Schrijver, A.: Combinatorial Optimization. Wiley, Chichester (1997)Google Scholar
  3. 3.
    Edmonds, J.: Matroids and the greedy algorithm. Math. Programming 1, 127–136 (1971)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Feige, U.: A threshold of ln n for approximating set cover. J. ACM 45, 634–652 (1998)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)MATHGoogle Scholar
  6. 6.
    Gopalan, P., Kolaitis, P.G., Maneva, E.N., Papadimitriou, C.H.: The connectivity of Boolean satisfiability: computational and structural dichotomies. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 346–357. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Håstad, J.: Clique is hard to approximate within n 1 − ε. Acta Mathematica 182, 105–142 (1999)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Håstad, J.: Some optimal inapproximability results. J. ACM 48, 798–859 (2001)MATHMathSciNetGoogle Scholar
  9. 9.
    Hearn, R.A., Demaine, E.D.: PSPACE-completeness of sliding-block puzzles and other problems through the nondeterministic constraint logic model of computation. Theoretical Computer Science 343, 72–96 (2005)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Ito, T., Zhou, X., Nishizeki, T.: Partitioning trees of supply and demand. International J. Foundations of Computer Science 16, 803–827 (2005)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Ito, T., Demaine, E.D., Zhou, X., Nishizeki, T.: Approximability of partitioning graphs with supply and demand. In: Asano, T. (ed.) ISAAC 2006. LNCS, vol. 4288, pp. 121–130. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994)MATHGoogle Scholar
  13. 13.
    Savitch, W.J.: Relationships between nondeterministic and deterministic tape complexities. J. of Computer and System Sciences 4, 177–192 (1970)MATHMathSciNetGoogle Scholar
  14. 14.
    Schaefer, T.J.: The complexity of satisfiability problems. In: Proc. of 10th ACM Symposium on Theory of Computing, pp. 216–226 (1978)Google Scholar
  15. 15.
    Schrijver, A.: Combinatorial Optimization: Polyhedra and Efficiency. Springer, Heidelberg (2003)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Takehiro Ito
    • 1
  • Erik D. Demaine
    • 2
  • Nicholas J. A. Harvey
    • 2
  • Christos H. Papadimitriou
    • 3
  • Martha Sideri
    • 4
  • Ryuhei Uehara
    • 5
  • Yushi Uno
    • 6
  1. 1.Graduate School of Information SciencesTohoku UniversitySendaiJapan
  2. 2.MIT Computer Science and Artificial Intelligence LaboratoryCambridgeUSA
  3. 3.Computer Science DivisionUniversity of California at BerkeleyBerkeleyUSA
  4. 4.Department of Computer ScienceAthens University of Economics and BusinessAthensGreece
  5. 5.School of Information ScienceJAISTIshikawaJapan
  6. 6.Graduate School of ScienceOsaka Prefecture UniversitySakaiJapan

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