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Maximum Flows and Minimum Cuts in the Plane

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Advances in Applied Mathematics and Global Optimization

Part of the book series: Advances in Mechanics and Mathematics ((AMMA,volume 17))

Summary

A continuous maximum flow problem finds the largest t such that div v = t F (x, y) is possible with a capacity constraint ||(v 1 v 2)|| ≤ c(x, y). The dual problem finds a minimum cut ∂ S which is filled to capacity by the flow through it. This model problem has found increasing application in medical imaging, and the theory continues to develop (along with new algorithms). Remaining difficulties include explicit streamlines for the maximum flow, and constraints that are analogous to a directed graph.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, 02139, Cambridge, MA, U.S.A

    Gilbert Strang

Authors
  1. Gilbert Strang
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Correspondence to Gilbert Strang .

Editor information

Editors and Affiliations

  1. Dept. Mathematics, Virginia Tech, McBryde Hall 524, Blacksburg, 24061, U.S.A.

    David Y. Gao

  2. State University, Dept. Industrial & Systems Engineering, Virginia Polytechnic Institute &, Whittemore Hall 547, Blacksburg, 24061, U.S.A.

    Hanif D. Sherali

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Strang, G. (2009). Maximum Flows and Minimum Cuts in the Plane. In: Gao, D., Sherali, H. (eds) Advances in Applied Mathematics and Global Optimization. Advances in Mechanics and Mathematics, vol 17. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-75714-8_1

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