Comparing two probabilistic models of the computational complexity of the branch and bound algorithm

  • Michèle Dion
  • Marc Gengler
  • Stéphane Ubéda
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 854)


We study two probabilistic models developed in order to predict the computational complexity of the branch and bound algorithm as well as its suitability for a parallelization based on the simultaneous exploration of all subproblems having a same common lower bound We show that both models, starting from different assumptions, yield asymptotically the same results but differ for small problems. Both models agree to predict a quick increase of the number of subproblems as a function of their lower bounds offering a convenient approach for parallelization of the branch and bound algorithm.


Branch and bound algorithm combinatorial optimization complexity modelization parallel computing 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Garey, M. R., Johnson, D. S.: Computers and Intractability — A Guide to the Theory of NP-Completeness. W. H. Freeman (1979)Google Scholar
  2. 2.
    Gengler, M., Coray, G.: A Parallel Best-first B&B with Synchronization Phases. Proceedings CONPAR'92-VAPP V, LNCS 634 (1992) 515–526Google Scholar
  3. 3.
    Gengler, M., Coray, G.: A Parallel Best-first B&B Algorithm and its Axiomatization. IEEE Proceedings HICSS-26, Vol. 2 (1993) 263–272Google Scholar
  4. 4.
    Johnson, D. S.: A Catalog of Complexity Classes. Algorithms and Complexity Vol. A, J. Van Leeuwen (ed.), Elsevier & MIT Press (1990) 67–161Google Scholar
  5. 5.
    Mitten, L. G.: Branch and Bound Methods: General Formulation and Properties. Operations Research 18 (1970) 24–34Google Scholar
  6. 6.
    Rinnooy Kan, A. H. G.: On Mitten's Axioms for Branch and Bound. Graduate School of Management, Delft, Tech. Rep. W/74/45/03 (1974)Google Scholar
  7. 7.
    Quinn, M. J.: Designing Efficient Algorithms for Parallel Computers. McGraw-Hill (1987)Google Scholar
  8. 8.
    Wah, B. W., Yu, C. F.: Probabilistic Modeling of Branch and Bound Algorithms. Proceedings COMPSAC (1982) 647–653Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Michèle Dion
    • 1
  • Marc Gengler
    • 2
  • Stéphane Ubéda
    • 3
  1. 1.Laboratoire de l'Informatique du ParallélismeEcole Normale Supérieure - LyonLyonFrance
  2. 2.Laboratoire d'Informatique Théorique, Ecublens (IN)Ecole Polytechnique Fédérale de LausanneLausanneSwitzerland
  3. 3.Laboratoire de Traitement du Signal et InstrumentationUniversité de Saint-EtienneSaint-EtienneFrance

Personalised recommendations