On the complexity of reconfiguration problems

Authors:
Takehiro Ito;Erik D. Demaine;Nicholas J. A. Harvey;Christos H. Papadimitriou;Martha Sideri;Ryuhei Uehara;Yushi Uno
Affiliations:
Graduate School of Information Sciences, Tohoku University, Aoba-yama 6-6-05, Sendai, 980-8579, Japan;MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar St., Cambridge, MA 02139, USA;Department of Combinatorics and Optimization, University of Waterloo, 200 University Ave. West, Waterloo, Ontario N2L 3G1, Canada;Computer Science Division, University of California at Berkeley, Soda Hall 689, EECS Department, Berkeley, CA 94720, USA;Department of Computer Science, Athens University of Economics and Business, Patision 76, Athens 10434, Greece;School of Information Science, JAIST, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan;Graduate School of Science, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai 599-8531, Japan
Venue:
Theoretical Computer Science
Year:
2011

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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.