  Comparability graphs are the undirected graphs whose edges can be directed so
that the resulting directed graph is transitive. They are related to posets and
have applications in scheduling theory. This paper considers the problem of
finding a transitive orientation of a comparability graph, a requirement for
many of its applications. A linear-time algorithm is presented based on an
elegant partition refinement scheme developed elsewhere for the problem. The
algorithm is intended as a simpler and more practical alternative to the
existing lineartime solution, which is commonly understood to be difficult and
mainly of theoretical value. It accomplishes this by using Lexicographic
Breadth-First Search to achieve the same effect as produced by modular
decomposition in the earlier linear-time algorithm.
