We introduce a subclass of NP optimization problems which contains, e.g., Bin Covering and Bin Packing. For each problem in this subclass we prove that with probability tending to 1 as the number of input items tends to infinity, the problem is approximable up to any given constant factor ε > 0 by a finite-state machine. More precisely, let II be a problem in our subclass of NP optimization problems, and let I be an input represented by a sequence of n independent identically distributed random variables with a fixed distribution. Then for any ε > 0 there exists a finite-state machine which does the following: On a random input I the finite-state machine produces a feasible solution whose objective value M(I) satisfies (Formula Presented)when n is large enough. Here K and h are positive constants.
CITATION STYLE
Hong, D., & Birget, J. C. (1997). Probabilistic approximation of some NP optimization problems by finite-state machines. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1269, pp. 151–164). Springer Verlag. https://doi.org/10.1007/3-540-63248-4_13
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