  We study computational aspects of the nonparametric maximum likelihood
estimator (NPMLE) for the distribution function of bivariate interval censored
data. The computation of the NPMLE consists of two steps: a parameter reduction
step and an optimization step. In this paper we focus on the reduction step. We
introduce two new reduction algorithms: the Tree algorithm and the HeightMap
algorithm. The Tree algorithm is only mentioned briefly. The HeightMap
algorithm is discussed in detail and also given in pseudo code. It is a very
fast and simple algorithm of time complexity O(n^2). This is an order faster
than the best known algorithm thus far, the O(n^3) algorithm of Bogaerts and
Lesaffre (2003). We compare our algorithms with the algorithms of Gentleman and
Vandal (2001), Song (2001) and Bogaerts and Lesaffre (2003), using simulated
data. We show that our algorithms, and especially the HeightMap algorithm, are
significantly faster. Finally, we point out that the HeightMap algorithm can be
easily generalized to d-dimensional data with d>2. Such a multivariate version
of the HeightMap algorithm has time complexity O(n^d).
