Using Nondeterminism to Design Efficient Deterministic Algorithms

  • Jianer Chen
  • Donald K. Friesen
  • Weijia Jia
  • Iyad A. Kanj
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2245)


In this paper, we illustrate how nondeterminism can be used conveniently and effectively in designing efficient deterministic algorithms. In particular, our method gives an O((5.7k)k n) parameterized algorithm for the 3-D matching problem, which significantly improves the previous algorithm by Downey, Fellows, and Koblitz. The algorithm can be generalized to yield an improved algorithm for the r-D matching problem for any positive integer r. The method can also be employed in designing deterministic algorithms for other optimization problems as well.


Bipartite Graph Match Problem Vertex Cover Deterministic Algorithm Maximal Match 
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.
    J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, North-Holland, New York, 1976.Google Scholar
  2. 2.
    J. Chen, I. A. Kanj, and W. Jia, “Vertex Cover: further observations and further improvements,” in Proc. 25th Int. Workshop on Graph-Theoretic Concepts in Computer Science, Lecture Notes in Computer Science, vol. 1665, pp. 313–324, Ascona, Switzerland, June 1999.Google Scholar
  3. 3.
    J. Chen, D. K. Friesen, W. Jia, and I. A. Kanj, “Using nondeterminism to design efficient deterministic algorithms,” Technical Report, Department of Computer Science, Texas A&M University, College Station, Texas, May 2001.Google Scholar
  4. 4.
    R. G. Downey and M. R. Fellows, Parameterized Complexity, New York, New York: Springer, (1999), pp. 220–222.Google Scholar
  5. 5.
    M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, 1979.zbMATHGoogle Scholar
  6. 6.
    R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, 1994.zbMATHGoogle Scholar
  7. 7.
    J. E. Hopcroft and R. M. Karp, An n 5/2 algorithm for maximum matching in bipartite graphs, SIAM J.Comput. 2, (1973), pp. 225–231.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    V. Kann, Maximum bounded 3-dimensional matching is MAX SNP-complete, Information Processing Letters 37, (1991), pp. 27–35.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Jianer Chen
    • 1
  • Donald K. Friesen
    • 1
  • Weijia Jia
    • 2
  • Iyad A. Kanj
    • 3
  1. 1.Department of Computer ScienceTexas A&M University
  2. 2.Department of Computer ScienceCity University of Hong KongKowloonHong Kong SAR, China
  3. 3.DePaul University, School of CTIChicago

Personalised recommendations