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Solving the minimum cut problem for undirected graphs
April 16, 2024 Di Wang, Research Scientist, Google Research We discuss a recent (best-paper award) publication at ACM-SIAM Symposium on Discrete Algorithms (SODA24) which gives a near-linear running time deterministic algorithm for the fundamental optimization problem of finding a minimum cut in weighted graphs. A graph is a ubiquitous data structure used in computer science that consists of nodes (or vertices) and edges between pairs of nodes to capture objects and their relations.
The minimum cut problem(often referred to as “min-cut”) is a basic structural question about the connectivity of a graph that asks: what is the least expensive way to disconnect a network? Moreover, min-cut has diverse applications in practice such as image restoration, stereo and segmentation in computer vision, and network resilience analysis (such as for roads or power grids). In particular, a seminal result by Karger in 1996 gave a nearly-linear time randomized algorithm that finds a min-cut with high probability, and a critical insight from that work was the existence of a much smaller graph that largely preserves all cuts’ size.
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