Maximum flows and minimum cuts in the plane
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 increasin...
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Springer-Verlag
2018
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| Online Access: | http://hdl.handle.net/1721.1/116027 |
| _version_ | 1826217561528729600 |
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| author | Strang, Gilbert |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Strang, Gilbert |
| author_sort | Strang, Gilbert |
| collection | MIT |
| description | 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 |
| first_indexed | 2024-09-23T17:05:38Z |
| format | Article |
| id | mit-1721.1/116027 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T17:05:38Z |
| publishDate | 2018 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/1160272022-09-29T23:38:27Z Maximum flows and minimum cuts in the plane Strang, Gilbert Massachusetts Institute of Technology. Department of Mathematics Strang, Gilbert 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 2018-05-31T17:46:39Z 2018-05-31T17:46:39Z 2009-09 2018-05-30T18:07:01Z Article http://purl.org/eprint/type/JournalArticle 0925-5001 1573-2916 http://hdl.handle.net/1721.1/116027 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 http://dx.doi.org/10.1007/s10898-009-9471-6 Journal of Global Optimization Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Springer-Verlag MIT Web Domain |
| spellingShingle | Strang, Gilbert Maximum flows and minimum cuts in the plane |
| title | Maximum flows and minimum cuts in the plane |
| title_full | Maximum flows and minimum cuts in the plane |
| title_fullStr | Maximum flows and minimum cuts in the plane |
| title_full_unstemmed | Maximum flows and minimum cuts in the plane |
| title_short | Maximum flows and minimum cuts in the plane |
| title_sort | maximum flows and minimum cuts in the plane |
| url | http://hdl.handle.net/1721.1/116027 |
| work_keys_str_mv | AT stranggilbert maximumflowsandminimumcutsintheplane |