Advertisement

Efficient on-line algorithms for the knapsack problem

Extended Abstract
  • Alberto Marchetti-Spaccamela
  • Carlo Vercellis
Algorithms And Complexity
Part of the Lecture Notes in Computer Science book series (LNCS, volume 267)

Abstract

Given a {0,1} or a relaxed knapsack problem with coefficients randomly chosen between zero and one, the behaviour of on-line algorithms will be analysed. In particular, a linear time on-line algorithm is proposed for which the expected difference between the optimum and the approximate solution value is 0(log3/2n). It is also shown that a Θ(1) lower bound on the expected difference between the optimum and the solution found by any on-line algorithm holds.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [CL86]
    Coffman, E.G. and F.T. Leighton, A provably efficient algorithm for dynamic storage allocation, Proc. 18th Ann. ACM Symp. on Theory of Computing, ACM, New York, 1986, 77–88.Google Scholar
  2. [FC84]
    Frieze, A.M. and M.R.B. Clarke, Approximation algorithms for the m-dimensional 0–1 knapsack problem: worst-case and probabilistic analysis. Eur. J. Oper. Res. 15 (1984), 100–109.Google Scholar
  3. [GMS84]
    Goldberg, A.V. and A. Marchetti-Spaccamela, On finding the exact solution of a 0–1 knapsack problem, Proc. 16th Ann. ACM Symp. on Theory of Computing, ACM, New York, 1984, 359–368.Google Scholar
  4. [H63]
    Hoeffding, W., Probability inequalities for sums of bounded random variables, Am. Stat. Ass. J. 3 (1963), 13–30.Google Scholar
  5. [HS78]
    Horowitz, E. and S. Sahni, Fundamentals of computer algorithms, Computer Science Press, 1978.Google Scholar
  6. [IK75]
    Ibarra, O.H. and C.E. Kim, Fast approximation algorithms for the knapsack and sum of subset problems, J. ACM 22 (1975), 463–468.Google Scholar
  7. [J74]
    Johnson, D.S., Approximation algorithms for combinatorial problems, J. of Comp. and System Sci. 9 (1974), 256–278.Google Scholar
  8. [K72]
    Karp, R.M., Reducibility among combinatorial problems, in Complexity of computer computations, R.E. Miller and J.W. Traub eds., Plenum Press, New York, 1972.Google Scholar
  9. [L77]
    Lawler, E.L., Fast approximation schemes for knapsack problems, Proc. 18th Conf. on Foundations of Computer Science, IEEE Computer Soc., New York, 1977, 206–213.Google Scholar
  10. [L82]
    Lueker, G.S., On the average difference between the solution to linear and integer knapsack problems, in Applied Probability-Computer Science: the Interface, Vol. I, Birkhauser, 1982.Google Scholar
  11. [MRKSV86]
    Meanti, M., A.H.G. Rinnooy Kan, L. Stougie and C. Vercellis, A probabilistic analysis of the multiknapsack value function, 1986, submitted to Mathematical Programming.Google Scholar
  12. [S84]
    Shor, P., The average-case analysis of some on-line algorithms for bin-packing, Proc. 25th Conf. on Foundations of Computer Science, IEEE Computer Soc., New York, 1984, 193–200.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Alberto Marchetti-Spaccamela
    • 1
  • Carlo Vercellis
    • 2
  1. 1.Dip. di Informatica e SistemisticaUniversitä di RomaRomaItaly
  2. 2.Dip. di Scienze dell'informazioneUniversità di MilanoMilanoItaly

Personalised recommendations