  In this survey paper, we will present a number of core algorithmic questions
concerning several transitive reduction problems on network that have
applications in network synthesis and analysis involving cellular processes.
Our starting point will be the so-called minimum equivalent digraph problem, a
classic computational problem in combinatorial algorithms. We will subsequently
consider a few non-trivial extensions or generalizations of this problem
motivated by applications in systems biology. We will then discuss the
applications of these algorithmic methodologies in the context of three major
biological research questions: synthesizing and simplifying signal transduction
networks, analyzing disease networks, and measuring redundancy of biological
networks.
