Finding and counting minimum cuts in graphs can be useful in image processing and segmentation and in networking systems such as computer or road networks. Researchers have previously developed polynomial-time algorithms to count minimum cuts in planar graphs which utilize the relationship between maximum network flows and minimum cuts.
This thesis presents a polynomial-time algorithm to count the number of minimum (s,t)-cuts in a planar graph without first finding a maximum flow. The presented algorithm is dependent on the finding that (s,t)-cuts in a planar graph correlate to certain cycles found in the dual of that graph, which can be efficiently counted.
Library of Congress Subject Headings
Graph theory; Algorithms; Combinatorial analysis
Computer Science (MS)
Department, Program, or Center
Computer Science (GCCIS)
Silva, Rachel E., "An Alternative Approach to Counting Minimum (s; t)-cuts in Planar Graphs" (2017). Thesis. Rochester Institute of Technology. Accessed from
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