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Probabilistic approximation of some NP optimization problems by finite-state machines

  • Dawei Hong
  • Jean-Camille Birget
Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1269)

Abstract

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
$$P\left( {\frac{{|Opt(I) - M(I)|}}{{\max \{ Opt(I),M(I)\} }} \geqslant \varepsilon } \right) \leqslant K\exp ( - hn)$$
when n is large enough. Here K and h are positive constants.

Keywords

NP- optimization problems approximation probabilistic algorithms finite-state machines 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Dawei Hong
    • 1
  • Jean-Camille Birget
    • 2
  1. 1.Dept. of Math. & Computer ScienceSouthwest State UniversityMarshallUSA
  2. 2.Dept. of Computer Science & Eng.University of NebraskaLincolnUSA

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