Maximum flows and minimum cuts in the plane
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maxminplane.pdf
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121.01 KB
Format
Adobe PDF
Checksum (MD5)
7d0ac4939be003e8d8ed7c80dd468f97
Author(s)
Strang, Gilbert
Date Issued
September 2009
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
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
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10898-009-9471-6
