On universally easy classes for NP-complete problems

Authors:
Erik D. Demaine;Alejandro López-Ortiz;J. Ian Munro
Affiliations:
Department of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada;Faculty of Computer Science, University of New Brunswick, P. O. Box 4400, Fredericton, N. B. E3B 5A3, Canada;Department of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Venue:
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Year:
2001

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Note: on universally easy classes for NP-complete problems

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Abstract

We explore the natural question of whether all NP-complete problems have a common restriction under which they are polynomially solvable. More precisely, we study what languages are universally easy in that their intersection with any NP-complete problem is in P. In particular, we give a polynomial-time algorithm to determine whether a regular language is universally easy. While our approach is language-theoretic, the results bear directly on finding polynomial-time solutions to very broad and useful classes of problems.