On the Complexity of Reconfiguration Problems

Authors:
Takehiro Ito;Erik D. Demaine;Nicholas J. Harvey;Christos H. Papadimitriou;Martha Sideri;Ryuhei Uehara;Yushi Uno
Affiliations:
Graduate School of Information Sciences, Tohoku University, Sendai, Japan 980-8579;MIT Computer Science and Artificial Intelligence Laboratory, Cambridge, USA MA 02139;MIT Computer Science and Artificial Intelligence Laboratory, Cambridge, USA MA 02139;Computer Science Division, University of California at Berkeley, Berkeley, USA CA 94720;Department of Computer Science, Athens University of Economics and Business, Athens, Greece 10434;School of Information Science, JAIST, Ishikawa, Japan 923-1292;Graduate School of Science, Osaka Prefecture University, Sakai, Japan 599-8531
Venue:
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Year:
2008

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Abstract

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.