Many problems in bioinformatics are inference problems, that is, the problem objective is to infer something based upon a limited amount of information. In this work we explore two different inference problems in bioinformatics. The first problem is inferring the structure of signal transduction networks from interactions between pairs of cellular components. We present two contributions towards the solution to this problem: an mixed integer program that produces and exact solution, and an implementation of an approximation algorithm in Java that was originally described by DasGupta et al. An exact solution is obtained for a problem instance consisting of real data. The second problem this thesis examines is the problem of inferring complete haplotypes from informative SNPs. In this work we describe two variations of the linear algebraic method for haplotype prediction and tag SNP selection: Two different variants of the algorithm are described and implemented, and the results summarized.