Implementing branch-and-bound in a ring of processors

  • Oliver Vornberger
Nonnumerical Algorithms (Session 2.2)
Part of the Lecture Notes in Computer Science book series (LNCS, volume 237)


A set of personal computers is connected to form a ring structured parallel system: Each processor has access to its local memory and can exchange messages with its two ring neighbors.

A branch-and-bound procedure is implemented in Pascal to run in parallel on the ring and solve the Travelling-Salesman-Problem. Heuristics are developed to maintain a priority queue in a distributed heap. The computing times and speedups for 25 random graphs obtained with up to 16 ring members are discussed.


Travel Salesman Problem Hamiltonian Cycle Global Memory Priority Queue Multiprocessor System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

8. References

  1. [1]
    Finkel, R. and U. Manber, 1983, "DIB — A Distributed Implementation of Backtracking", Computer Science Technical Report #583, University of Wisconsin, MadisonGoogle Scholar
  2. [2]
    Garey, M.R. and D.S. Johnson, 1979, "Computers and Intractability: A Guide to the Theory of NP-Completeness", Freeman, San Francisco, Calif.Google Scholar
  3. [3]
    Held, M. and R. Karp, 1971, "The Travelling Salesman Problem and Minimum Spanning Trees: Part II", Math. Prog. 1, pp. 6–25CrossRefGoogle Scholar
  4. [4]
    Lai, T.-H. and S. Sahni, 1984, "Anomalies in Parallel Branch-and-Bound Algorithms", Communications of the ACM, Vol. 27, No. 6, pp. 594–602CrossRefGoogle Scholar
  5. [5]
    Lawler, E.-L. and D.E. Wood, 1966, "Branch-and-Bound Methods: A survey", Operations Research 14, pp. 699–719Google Scholar
  6. [6]
    Li, G. and B.W. Wah, 1984, "Computational Efficiency of Parallel Approximate Branch-and-Bound Algorithms", Proc. of the 1984 International Conference on Parallel Processing, pp. 473–480Google Scholar
  7. [7]
    Mohan, J. 1983, "A study in Parallel Computations: the Travelling Saelsman Problem", Technical Report CMU-CS-82-136(R), Dept. of Computer Science, Carnegie-Mellon University, PittsburghGoogle Scholar
  8. [8]
    Monien, B., E. Speckenmeyer, O. Vornberger, 1986, "Superlinear Speedup for parallel Backtracking", submitted for publicationGoogle Scholar
  9. [9]
    Monien, B., O. Vornberger, 1986, "The Ring Machine", submitted for publicationGoogle Scholar
  10. [10]
    Vornberger, O., 1986, "Implementing Branch-and-Bound in a Ring of Processors", Technical Report Nr. 29, Dept. of Mathematics and Computer Science, University of Paderborn, W.-GermanyGoogle Scholar
  11. [11]
    Wah, B.W. and Y.W. Eva Ma, 1984, "MANIP — A Multicomputer Architecture for Solving Combinatorial Extremum-Search Problems", IEEE Transactions on Computers, Vol. C-33, No. 5, pp. 377–390Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Oliver Vornberger
    • 1
  1. 1.Dept. of Mathematics & Computer ScienceUniversity of PaderbornWest — Germany

Personalised recommendations