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Theory of Equal-Flows in Networks

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Computing and Combinatorics (COCOON 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2387))

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Abstract

The Maximum-Flow problem is a classical problem in combinatorial optimization and has many practical applications. We introduce a new variant of this well known Maximum-Flow problem, viz., the Maximum-Equal-Flow problem,wherein, for each vertex (other than the source) in the network, the actual flows along the arcs emanating from that vertex are constrained to be equal and integral. Surprisingly, unlike the Maximum-Flow problem that is known to admit a polynomial time solution, we prove that the Maximum-Equal-Flow problem is NP-Hard. Nevertheless, we provide an approximation algorithm for the Maximum-Equal-Flow problem. We develop a new (analogous) theory for Equal-Flows in networks and also illustrate the Maximum-Equal-Flow equivalents of the fundamental results in flow theory.

Financial support from Infosys Technologies Limited, India, is acknowledged.

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References

  1. P. Elias, A. Feinstein, and C. E. Shannon. Note on maximum flow through a network. IRE Trans. Information Theory, IT-2, 1956.

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  2. L. R. Ford and D. R. Fulkerson. Flows in Networks. Princeton University Press, Princeton, N. J., 1962.

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Author information

Author notes

  1. R. Nandakumar

    Present address: University of Chicago, USA

Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, Madras, Chennai, 600036, India

    K. Srinathan, Pranava R. Goundan, M. V. N. Ashwin Kumar, R. Nandakumar & C. Pandu Rangan

Authors
  1. K. Srinathan
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  2. Pranava R. Goundan
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  3. M. V. N. Ashwin Kumar
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  4. R. Nandakumar
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  5. C. Pandu Rangan
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of California, Santa Barbara, California, 93106, USA

    Oscar H. Ibarra

  2. Department of Mathematics, National University of Singapore, Singapore, Singapore, 117543

    Louxin Zhang

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© 2002 Springer-Verlag Berlin Heidelberg

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Cite this paper

Srinathan, K., Goundan, P.R., Kumar, M.V.N.A., Nandakumar, R., Rangan, C.P. (2002). Theory of Equal-Flows in Networks. In: Ibarra, O.H., Zhang, L. (eds) Computing and Combinatorics. COCOON 2002. Lecture Notes in Computer Science, vol 2387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45655-4_55

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  • DOI: https://doi.org/10.1007/3-540-45655-4_55

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43996-7

  • Online ISBN: 978-3-540-45655-1

  • eBook Packages: Springer Book Archive

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