Many bioinformatics problems are inference problems: Given partial or incomplete information about something, use that information to infer the missing or unknown data. This work addresses two inference problems in bioinformatics. The rst problem is inferring viral quasispecies sequences and their frequencies from 454 pyrosequencing reads. The second problem is inferring the structure of signal transduction networks from observations of interactions between cellular components. At first glance, these problems appear to be unrelated to each other. However, this work successfully penetrates both problems using the machinery of ow networks and transitive reduction, tools from classical computer science that prove useful in a wide array of application domains.