In the vertex connectivity survivable network design problem we are given an
undirected graph G = (V,E) and connectivity requirement r(u,v) for each pair of
vertices u,v. We are also given a cost function on the set of edges. Our goal
is to find the minimum cost subset of edges such that for every pair (u,v) of
vertices we have r(u,v) vertex disjoint paths in the graph induced by the
chosen edges. Recently, Chuzhoy and Khanna presented a randomized algorithm
that achieves a factor of O(k^3 log n) for this problem where k is the maximum
connectivity requirement. In this paper we derandomize their algorithm to get a
deterministic O(k^3 log n) factor algorithm. Another problem of interest is the
single source version of the problem, where there is a special vertex s and all
non-zero connectivity requirements must involve s. We also give a deterministic
O(k^2 log n) algorithm for this problem