arXiv Computer Vision By Christian M{\o}ller Mikkelstrup, Anders Bjorholm Dahl, Philip Bille, Vedrana Andersen Dahl, Inge Li G{\o}rtz

Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm

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The paper revisits the Boykov‑Kolmogorov (BK) algorithm for computing minimum s‑t cuts in graphs, improving its theoretical time complexity to O(mn|C|). It introduces a faster variant, the fast BK (fBK) algorithm, with complexity O(m|C|), and proposes a compact graph representation enabling the algorithms to handle graphs with up to 10^9 vertices and 10^10 edges on a 128 GB machine. Experiments show that the compact BK implementation (cBK) outperforms other BK variants, underscoring the value of memory‑efficient designs.

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