From Static Code Distribution to More Shrinkage for the Multiterminal Cut

  • Bram De Wachter
  • Alexandre Genon
  • Thierry Massart
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3503)


We present the problem of statically distributing instructions of a common programming language, a problem which we prove equivalent to the multiterminal cut problem.  We design efficient shrinkage techniques which allow to reduce the size of an instance in such a way that optimal solutions are preserved. We design and evaluate a fast local heuristics that yields remarkably good results compared to a well known \(2-\frac{2}{k}\) approximation algorithm. The use of the shrinkage criterion allows us to increase the size of the instances solved exactly, or to augments the precision of any particular heuristics.


Approximation Algorithm Grammar Graph Weighted Undirected Graph Industrial Control System Polynomial Time Reduction 
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.


  1. 1.
    Massart, T., DeWachter, B., Genon, A.: From static code distribution to more shrinkage for the multiterminal cut. Technical Report 007, U.L.B. (December 2004)Google Scholar
  2. 2.
    Calinescu, G., Karloff, H., Rabani, Y.: An improved approximation algorithm for multiway cut. J. Comput. Syst. Sci. 60(3), 564–574 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Chopra, S., Owen, J.H.: Extended formulations for the a-cut problem. Math. Program. 73, 7–30 (1996)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Costa, M., Letocart, L., Roupin, F.: Minimal multicut and maximal integer multiflow: a survey. European Journal of Operational Research 162(1), 55–69 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Cunningham, W.H.: The optimal multiterminal cut problem. DIMACS series in discrete mathematics and theoretical computer science 5, 105–120 (1991)MathSciNetGoogle Scholar
  6. 6.
    Vohra, R., Bertsimas, D., Teo, C.: Nonlinear formulations and improved randomized approximation algorithms for multicut problems. In: Balas, E., Clausen, J. (eds.) IPCO 1995. LNCS, vol. 920, pp. 29–39. Springer, Heidelberg (1995)Google Scholar
  7. 7.
    Dahlhaus, E., Johnson, D.S., Papadimitriou, C.H., Seymour, P.D., Yannakakis, M.: The complexity of multiterminal cuts. SIAM J. Comput. 23(4), 864–894 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Ford, L.R., Fulkerson, D.R.: Flows in Networks. Princeton University Press, Princeton (1962)zbMATHGoogle Scholar
  9. 9.
    Garg, N., Vazirani, V.V., Yannakakis, M.: Multiway cuts in directed and node weighted graphs. In: Proceedings of the 21st International Colloquium on Automata, Languages and Programming, pp. 487–498. Springer, Heidelberg (1994)Google Scholar
  10. 10.
    Goldberg, A.V., Tarjan, R.E.: A new approach to the maximum-flow problem. Journal of the ACM (JACM) 35(4), 921–940 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Hogstedt, K., Kimelman, D.: Graph cutting algorithms for distributed applications partitioning. SIGMETRICS Performance Evaluation Review 28(4), 27–29 (2001)CrossRefGoogle Scholar
  12. 12.
    Hollermann, L., Hsu, T.s., Lopez, D.R., Vertanen, K.: Scheduling problems in a practical allocation model. J. Comb. Optim. 1(2), 129–149 (1997)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Karger, D.R., Klein, P., Stein, C., Thorup, M., Young, N.E.: Rounding algorithms for a geometric embedding of minimum multiway cut. In: STOC 1999: Proceedings of the thirty-first annual ACM symposium on Theory of computing, pp. 668–678 (1999)Google Scholar
  14. 14.
    Naor, J., Zosin, L.: A 2-approximation algorithm for the directed multiway cut problem. SIAM J. Comput. 31(2), 477–482 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Rao, M.R., Chopra, S.: On the multiway cut polyhedron. Networks 21, 51–89 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Hsu, T.s., Lee, J.C., Lopez, D.R., Royce, W.A.: Task allocation on a network of processors. IEEE Trans. Computers 49(12), 1339–1353 (2000)CrossRefMathSciNetGoogle Scholar
  17. 17.
    De Wachter, B., Massart, T., Meuter, C.: dsl: An environment with automatic code distribution for industrial control systems. In: Papatriantafilou, M., Hunel, P. (eds.) OPODIS 2003. LNCS, vol. 3144, pp. 132–145. Springer, Heidelberg (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Bram De Wachter
    • 1
  • Alexandre Genon
    • 1
  • Thierry Massart
    • 1
  1. 1.Département d’InformatiqueUniversité Libre de BruxellesBruxelles

Personalised recommendations