A Generic Program for Minimal Subsets with Applications

  • Rudolf Berghammer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2664)


We formally develop a generic program which computes a minimal subset satisfying a certain property of a given set. To improve the efficiency of instantiations, refinements are investigated. Finally, instantiations are presented which correspond to the solution of well-known graph-theoretic problems and some further applications are sketched.


Generic Program Vertex Cover Input Graph Minimal Subset Maximal Subset 
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.
    R. Behnke et al. Applications of the Rel View system. In: R. Berghammer, Y. Lakhnech (eds.): Tool support for system specification, development and verification. Springer, pages 33–47, 1999.Google Scholar
  2. 2.
    R. Berghammer, B. von Karger, and C. Ulke. Relation-algebraic analysis of Petri nets with Rel View. In: T. Margaria, B. Steffen (eds.): Proc. 2nd Workshop on Tools and Applications for the Construction and Analysis of Systems, LNCS 1055, Springer, pages 49–69, 1996.Google Scholar
  3. 3.
    T.H. Cormen, C.E. Leiserson, and R.L. Rivest. Introduction to algorithms. The MIT Press, 1990.Google Scholar
  4. 4.
    E.W. Dijkstra. A discipline of programming. Prentice-Hall, 1976.Google Scholar
  5. 5.
    J. Edmonds. Paths, trees, and flowers. Canadian Journal of Mathematics 17:449–467, 1965.MATHMathSciNetGoogle Scholar
  6. 6.
    D. Gries. The science of computer programming. Springer, 1981.Google Scholar
  7. 7.
    P. Helman, B.M.E. Moret, H.D. Shapiro. An exact characterization of greedy structures. SIAM Journal Disc. Math. 6:274–283, 1993.MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    D. Hochbaum (ed.). Approximation algorithms for NP-hard problems. PWS Publishing Company, 1995.Google Scholar
  9. 9.
    J. Hopcroft and R. Tarjan. Efficient planarity testing. Journal of the ACM 21:549–568, 1974.MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    C. Kasper. Investigating algorithms for transitive reductions and minimum equivalent digraphs (in German). Diploma thesis, Institut für Informatik und Praktische Mathematik, Universität Kiel, 2001.Google Scholar
  11. 11.
    S. Khuller, B. Raghavachari, and N. Young. Approximating the minimum equivalent digraph. SIAM Journal of Computing 24:859–972, 1995.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    B. Leoniuk. ROBDD-based implementation of relations and relational operations with applications (in German). Ph.D. thesis, Institut für Informatik und Praktische Mathematik, Universität Kiel, 2001.Google Scholar
  13. 13.
    B.M.E. Moret and H.D. Shapiro. Algorithms and experiments: The new (and old) methodology. Journal of Universal Computer Science 7:434–446, 2001.MATHMathSciNetGoogle Scholar
  14. 14.
    B.M.E. Moret. Towards a discipline of experimental algorithmics. DIMACS Series in Discrete Mathematics and Theoretical Computer Science (to appear).Google Scholar
  15. 15.
    C. Morgan and T. Vickers (eds.). On the refinement calculus. Formal Approaches to Computing and Information Technology, Springer, 1992.Google Scholar
  16. 16.
    H. Noltemeier. Reduktion von Präzedenzstrukturen. Zeitschrift für Operations Research 20: 151–159, 1976.MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    J. Ravelo. Two graph algorithms derived. Acta Informatica 36:489–510, 1999.MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    R. Tamassia and T.G. Tollis. Planar grid embedding in linear time. IEEE Transactions on Circuits and Systems 36:1230–1234, 1989.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Rudolf Berghammer
    • 1
  1. 1.Institut für Informatik und Praktische MathematikChristian-Albrechts-Universität KielKielGermany

Personalised recommendations