Abstract
NP-completeness is, in a well-defined sense, a worst case notion. Thus, 3-colorability of a graph, for a randomly generated graph, can be determined in constant expected time even though the general problem is NP-complete. The reason for this is that some hard problems exhibit a structure where only a small (perhaps exponentially small) fraction of all possible instances is intractable, while the remaining large fraction has a polynomial time solution algorithm. We add a new problem to the list of NP-complete problems that are solvable in average polynomial time.
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© 1995 Springer-Verlag Berlin Heidelberg
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Havas, G., Majewski, B.S. (1995). A hard problem that is almost always easy. In: Staples, J., Eades, P., Katoh, N., Moffat, A. (eds) Algorithms and Computations. ISAAC 1995. Lecture Notes in Computer Science, vol 1004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015426
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DOI: https://doi.org/10.1007/BFb0015426
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