  We consider privacy preserving decision tree induction via ID3 in the case
where the training data is horizontally or vertically distributed. Furthermore,
we consider the same problem in the case where the data is both horizontally
and vertically distributed, a situation we refer to as grid partitioned data.
We give an algorithm for privacy preserving ID3 over horizontally partitioned
data involving more than two parties. For grid partitioned data, we discuss two
different evaluation methods for preserving privacy ID3, namely, first merging
horizontally and developing vertically or first merging vertically and next
developing horizontally. Next to introducing privacy preserving data mining
over grid-partitioned data, the main contribution of this paper is that we
show, by means of a complexity analysis that the former evaluation method is
the more efficient.
