Saturating flows in networks

  • B. S. Chlebus
  • M. Chrobak
  • K. Diks
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 278)


A saturating flow through a network satisfies the condition that if it uses an edge then it uses its whole capacity. We show that the problem to verify whether there is a non-zero saturating flow in a given network is strongly NP-complete. This problem restricted to edge series-parallel networks remains NP-complete, but there is a pseudopolynomial time algorithm solving it. Restricted still farther to s-t outerplanar networks the problem is polynomially solvable.


Planar Network Satisfying Assignment Outerplanar Graph Saturate Flow Minimum Cost Flow 


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  1. [BBT]
    W.W. Bein, P. Brucker, and A. Tamir, Minimum cost flow algorithms for series-parallel networks, Discr. Appl. Math. 10 (1985), 117–124.Google Scholar
  2. [CD]
    M. Chrobak, and K. Diks, Network flows in outerplanar networks, submitted.Google Scholar
  3. [EIS]
    S. Even, A, Itai, and A. Shamir, On the complexity of timetable and multicomodity flow problems, SIAM J. Computing 5 (1976), 691–703.Google Scholar
  4. [ET]
    S. Even, and R.E. Tarjan, Network flow and testing graph connectivity, SIAM J. Computing 4 (1975), 399–404.Google Scholar
  5. [GJ]
    M.R. Garey, and D.S. Johnson, "Computers and Intractability: A Guide to the Theory of NP-Completeness," W.H. Freeman, San Francisco, 1979.Google Scholar
  6. [HS]
    T.C. Hu, and M.T. Shing, Multiterminal flows in outerplanar networks, J. Algorithms 4 (1983), 241–261.Google Scholar
  7. [I]
    A. Itai, Two-commodity flow, Rep. No 93, Dept. of Comput. Sci., Technion, Haifa, Israel.Google Scholar
  8. [L]
    E.L. Lawler, "Combinatorial Optimization: Networks and Matroids," Holt, Rinehart and Winston, New York, 1976.Google Scholar
  9. [PS]
    C.H. Papadimitriou, and K. Steiglitz, "Combinatorial Optimization: Algorithms and Complexity," Prentice-Hall, Englewood Cliffs, New York, 1982.Google Scholar
  10. [S]
    S. Sahni, Computationally related problems, SIAM J. Computing 3 (1974), 262–279.Google Scholar
  11. [Sy]
    M.M. Syslo, Characterizations of outerplanar graphs, Disc. Math. 26 (1979), 47–53.Google Scholar
  12. [T]
    R.E. Tarjan, "Data Structures and Network Algorithms," SIAM, Philadelfia, Pennsylvania, 1983.Google Scholar
  13. [VTL]
    J. Valdes, R.E. Tarjan, and E.L. Lawler, The recognition of series-parallel networks, SIAM J. Computing 11 (1982), 298–313.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • B. S. Chlebus
    • 1
  • M. Chrobak
    • 1
  • K. Diks
    • 1
  1. 1.Institute of InformaticsWarsaw UniversityWarsawPoland

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