Table 1: Related work on computing minimum s-t link cuts.

Year1 Reference Complexity Description

1951 Dantzig [30] Linear programming, where is the largest link capacity.

1956 Ford and Fulkerson [31] Augmenting paths.

1970 Dinitz [27] , Resp. capacitated and unit-capacity graphs. Shortest augmenting paths.

1974 Karzanov [32] Preflow-push (A simplification of Karzanov's algorithm has been presented by Tarjan [33]).

1980 Galil and Naamad [34] Extension of Dinitz' algorithm.

1982 Shiloach and Vishkin [35] Parallel algorithm for processors.

1983 Sleator and Tarjan [36] Dynamic tree data structure.

1986 Goldberg and Tarjan [37] Highest-label preflow-push.

1987 Ahuja et al. [38] Excess scaling.

1989 Cheriyan and Hagerup [39] Randomized algorithm.

1990 Alon [40] Deterministic version of Cheriyan and Hagerup's randomized algorithm.

1998 Goldberg and Rao [41] Length function.

2011 Christiano et al. [42] , Resp. and approximation, where denotes for some constant .

1Throughout the paper, we take the convention of listing the year of the first (conference) publication, while referring to the extended (journal) version there where applicable.