Note: on universally easy classes for NP-complete problems

Authors:
Erik D. Demaine;Alejandro López-Ortiz;J. Ian Munro
Affiliations:
MIT Laboratory for Computer Science, 200 Technology Square, Cambridge, MA;Department of Computer Science, University of Waterloo, Waterloo, Ont., Canada N2L 3G1;Department of Computer Science, University of Waterloo, Waterloo, Ont., Canada N2L 3G1
Venue:
Theoretical Computer Science
Year:
2003

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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 (universally polynomial) or at least no longer NP-complete (universally simplifying). 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.