Table 3: Related work on augmenting link connectivity in unweighted graphs.

Year Reference Complexity Description

1976 Eswaran and Tarjan [54] Augmenting to 2-connectivity.

1986 Cai and Sun [75] NA Splitting off links.

1987 Watanabe and Nakamura [76] Based on a derived formula for the minimum number of links to -link-connect .

1990 Frank [77] Different s-t connectivities may be specified, instead of one -connectivity for all pairs1.

1990 Naor et al. [65] is the complexity of computing a maximum flow. If , then the complexity is .

1991 Gabow [78] Poset representation of cuts applied to the Naor-Gusfield-Martel algorithm.

1994 Benczúr [79] , Resp. randomized and deterministic algorithms.

1996 Nagamochi and Ibaraki [80] Splitting off links.

1998 Benczúr and Karger [81] Randomized algorithm.

2004 Nagamochi and Ibaraki [82] Maximum adjacency ordering2.

1NP-hard variations of this problem and corresponding approximation results are provided by Nutov [83].
2Maximum adjacency ordering rule: add a new node to previously selected nodes that has the largest number of links to the set . Start with an abitrary node .