The problem of finding a minimum weight k-vertex connected spanning subgrap
h in a graph G = (V, E) is considered. For k greater than or equal to 2, th
is problem is known to be NP-hard. Based on the paper of Auletta, Dinitz, N
utov, and Parente in this issue, we derive a 3-approximation algorithm for
k is an element of {4, 5}. This: improves the best previously known approxi
mation ratios 41/6 and 417/30, respectively. The complexity of the suggeste
d algorithm is O(/V/(5)) for the deterministic and O(/V/(4)log/V/) for the
randomized version. The way of solution is as follows. Analyzing a subgraph
constructed by the algorithm of the aforementioned paper, we prove that al
l its "small" cuts have exactly two sides and separate a certain fixed pair
of vertices. Such a subgraph is augmented to a k-connected one (optimally)
by at most four executions of a min-cost k-flow algorithm. (C) 1999 Academ
ic Press.