On universally easy classes for NP-complete problems

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 NPcomplete 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. Key words: Complexity theory, polynomial time, NP-completeness, classes of instances, universally polynomial, universally simplifying, regular languages

• Type: Conference
• Year: 2001
• Where: SODA
• Authors: Erik D. Demaine, Alejandro López-Ortiz, J. Ian Munro
• Keywords: Algorithms, NP-complete Problems, Polynomial-time Algorithm, Regular Languages, SODA 2001