Skip to main content
SpringerLink
Log in

Some Remarks on a Classification of Oracle-Type-Algorithms

  • Chapter
Numerische Methoden bei graphentheoretischen und kombinatorischen Problemen

Abstract

This paper deals with polynomial relations between different kinds of oracles for optimization problems over independence systems. Six different greedy algorithms as special oracle algorithms are also considered. A certain symmetry among problems and algorithms is established by dualization of independence systems.

Supported by Sonderforschungsbereich 21 (DFG), Institut für Operations Research, Universität Bonn and NSF Grant ENG 76-09936.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 49.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Edmonds, J. [ 1971 ]: Matroids and the Greedy Algorithms. Mathematical Programming 1, (1971),p.p. 127–136.

    Google Scholar 

  2. Edmonds, J., Fulkerson, D.R. [ 1970 ]: Bottleneck Extrema. Journal of Combinatorial Theory 8 (1970),p.p. 299–306.

    Google Scholar 

  3. Hausmann, D., Körte, B. [ 1977 ]: Lower Bounds on the Worst-Case Complexity of Some Oracle Algorithms. Working Paper no. 7757. Institut für Ökonometrie and Operations Research, Universität Bonn,(April 1977), to appear in: Discrete Mathematics.

    Google Scholar 

  4. Hausmann, D., Körte, B. [ 1978a ]: Worst-Case Analysis for a Class of Combinatorial Optimizations Algorithms. in: J. Stoer (ed.): Optimization Techniques, Part 2, Lecture Notes in Control and Information Sciences,Vol.7. Springer Verlag Berlin/Heidelberg/New York (1978), p.p. 216–224.

    Google Scholar 

  5. Hausmann, D., Körte, B. [ 1978b ]: Oracle Algorithms for Fixed-Point Problems–An Axiomatic Approach. in: R. Henn, B. Körte, W. Oettli (eds.): Optimization and Operations Research. Lecture Notes in Economics and Mathematical Systems, Vol. 157, Springer Verlag Berlin/ Heidelberg/New York (1978), p.p. 137–156.

    Google Scholar 

  6. Hausmann, D., Kannan, R., Körte, B. [ 1977 ]: Exponential Lower Bounds on a Class of Knapsack Algorithms. Working Paper no. 7789. Institut für Ökonometrie and Operations Research, Universität Bonn,(December 1977 ).

    Google Scholar 

  7. Jenkyns, Th.A. [ 1976 ]: The Efficacy of the “Greedy” Algorithm. Proc. 7th S.-E. Conf. Combinatorics, Graph Theory, and Computing, (1976),p.p. 341–350.

    Google Scholar 

  8. Kannan, R., Körte, B. [ 1978 ]: Approximative Combinatorial Algorithms. Working Paper 78107–0R. Institut für Ökonometrie and Operations Research, Universität Bonn, (July 1978), to appear in: Proceedings Summer School on Combinatorial Optimization, Urbino, Italy.

    Google Scholar 

  9. Körte, B. [1977]: Approximative Algorithms for Discrete Optimization Problems. Working Paper no. 7762-OR. Institut für Ökonometrie and Operations Research, Universität Bonn, (1978), to appear in: Annais of Discrete Mathematics, Vol. 4.

    Google Scholar 

  10. Körte, B., Hausmann, D. [ 1978 ]: An Analysis of the Greedy Heuristic for Independence Systems, in: Alspach, B., Hell, P., Miller, D.J. (eds.): Algorithmic Aspects of Combinatorics. Annais of Discrete Mathematics 2 (1978), p.p. 65–74.

    Chapter  Google Scholar 

  11. Matthews, L. [1978]: Closure in Independence Systems. Wor king Paper 7894-OR. Institut für Ökonometrie and Operations Research, Universität Bonn, (1978).

    Google Scholar 

  12. Rado, R. [ 1957 ]: Note on Independence Functions. Proceedings London Mathematical Society 7 (1957),p.p. 300–320.

    Google Scholar 

  13. Sperner, E. [ 1928 ]: Ein Satz über Untermengen einer endli chen Menge. Mathematische Zeitschrift 27 (1928),p.p. 544–548.

    Google Scholar 

  14. Welsh, D.J.A. [ 1968 ]: Kruskals Theorem for Matroids. Proceedings Cambridge Phil. Soc. 64 (1968),p.p. 3–4.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Operations Research, Universität Bonn, Nassestr. 2, D-5300, Bonn 1, West Germany

    Professor Dr. Bernhard Korte & Clyde L. Monma Ph.D.

Authors
  1. Professor Dr. Bernhard Korte
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Clyde L. Monma Ph.D.
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Hamburg, Deutschland

    L. Collatz

  2. Siegen, Deutschland

    G. Meinardus

  3. Enschede, Niederlande

    W. Wetterling

Rights and permissions

Reprints and permissions

Copyright information

© 1979 Springer Basel AG

About this chapter

Cite this chapter

Korte, B., Monma, C.L. (1979). Some Remarks on a Classification of Oracle-Type-Algorithms. In: Collatz, L., Meinardus, G., Wetterling, W. (eds) Numerische Methoden bei graphentheoretischen und kombinatorischen Problemen. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 46. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5997-4_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-5997-4_13

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-1078-3

  • Online ISBN: 978-3-0348-5997-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation