Table 1:
Related work on computing minimum
s

t
link cuts.
Year
^{1}
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 unitcapacity graphs. Shortest augmenting paths.
1974
Karzanov [
32
]
Preflowpush (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
]
Highestlabel preflowpush.
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
.
^{ 1}
Throughout 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.