Restrictions of Graph Partition Problems

  • Hans L. Bodlaender
  • Klaus Jansen
Conference paper


Let J be a set of n jobs, all with job processing time or job length one, and let M be a set of k machines. Incompatibilities between jobs are described by an undirected graph G = (J, E) with vertex set J. If G contains an edge between two jobs j and j′ (jj′), we demand that these two jobs can not be executed by the same machine. An assignment of the jobs to the machines, which satisfies the incompatibility relation, is called a schedule. The processing time of a machine is given by the number of assigned jobs, since each job has processing time one.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D.G. Cornell, Y. Perl, and L.K. Stewart, A linear recognition algorithm for cographs, SIAM J. Comput. 4 (1985), pp. 926–934.CrossRefGoogle Scholar
  2. [2]
    M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, 1979.Google Scholar
  3. [3]
    M.C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press, London, 1980.Google Scholar
  4. [4]
    D.I. Gupta, D.T. Lee and J.Y.-T. Leung, Efficient algorithms for interval graphs and circular arc graphs, Networks 12 (1982), pp. 459–467.CrossRefGoogle Scholar
  5. [5]
    R.M. Karp, Reducibility among combinatorial problems, in: Miller and Thatcher: Complexity of Computer Computations, Plenum Press (1972), pp. 85–104.Google Scholar
  6. [6]
    Z. Lonc, On complexity of some chain and antichain partition problems, WG Conference, LNCS 570 (1991), pp. 97–104.Google Scholar
  7. [7]
    C.H. Papadimitriou and M. Yannakakis, Scheduling interval-ordered tasks, SIAM J. Comp. 8 (1979), pp. 405–409.CrossRefGoogle Scholar
  8. [8]
    D. Seinsche, On a property of the class of n-colorable graphs, J. Comb. Theory B 16 (1974), pp. 191–193.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Hans L. Bodlaender
    • 1
  • Klaus Jansen
    • 2
  1. 1.Department of Computer ScienceUtrecht UniverstiyUtrechtNetherlands
  2. 2.Fachbereich IV, Mathematik/InformatikUniversität TrierTrierGermany

Personalised recommendations