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Stochastic on-line knapsack problems

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Abstract

Different classes of on-line algorithms are developed and analyzed for the solution of {0, 1} and relaxed stochastic knapsack problems, in which both profit and size coefficients are random variables. In particular, a linear time on-line algorithm is proposed for which the expected difference between the optimum and the approximate solution value isO(log3/2 n). AnΩ(1) lower bound on the expected difference between the optimum and the solution found by any on-line algorithm is also shown to hold.

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Authors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”, Via Eudossiana 18, I-00184, Roma, Italy

    A. Marchetti-Spaccamela

  2. Dipartimento di Economia e Produzione, Politecnico di Milano, P.za L. da Vinci 32, I-20133, Milano, Italy

    C. Vercellis

Authors
  1. A. Marchetti-Spaccamela
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  2. C. Vercellis
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Corresponding author.

Partially supported by the Basic Research Action of the European Communities under Contract 3075 (Alcom).

Partially supported by research project “Models and Algorithms for Optimization” of the Italian Ministry of University and Scientific and Technological Research (MURST 40%).

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Marchetti-Spaccamela, A., Vercellis, C. Stochastic on-line knapsack problems. Mathematical Programming 68, 73–104 (1995). https://doi.org/10.1007/BF01585758

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  • DOI: https://doi.org/10.1007/BF01585758

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