With thousands of genes and dozens of experiments, the immense
amount of biological data produced by microarrays cannot be evaluated
purely by humans. Computer analysis and visualization of this information
is therefore an important area of research. This paper explores effi-
cient algorithms for one step of displaying such data in a way that it can
be analyzed by humans: ordering the genes on the display to best illustrate
trends in gene expression. A general formulation of this unrestricted
problem is computationally intractable (see Section 2.1). A natural alternative
approach, suggested by Eisen et al. [6], is to restrict the orderings
to those illustrating a high-quality hierarchical clustering of the genes
(see Figure 1). In such a diagram one can easily observe both the expression
profiles of similar genes and the clusters formed by the clustering
algorithm. As a consequence, this approach has been used successfully
to analyze many experiments; see for example [1, 14, 17, 21, 22] and many
others.