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Maximum flows and minimum cuts in the plane

Author(s)
Strang, Gilbert
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Abstract
A continuous maximum flow problem finds the largest t such that div v = t F(x, y) is possible with a capacity constraint ||(v[subscript 1], v[subscript 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. Keywords: Maximum flow; Minimum cut; Capacity constraint; Cheeger
Date issued
2009-09
URI
http://hdl.handle.net/1721.1/116027
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Journal of Global Optimization
Publisher
Springer-Verlag
Citation
Strang, Gilbert. “Maximum Flows and Minimum Cuts in the Plane.” Journal of Global Optimization 47, 3 (September 2009): 527–535 © 2009 Springer Science+Business Media
Version: Author's final manuscript
ISSN
0925-5001
1573-2916

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