We highlight three recent examples where the toolbox of computational discrete algorithms was crucial to the design and efficient implementation of our methods for inference in different settings involving protein-protein or genetic interaction networks. First we describe Approximate IsoRank, an approximation of the famous IsoRank method for global alignment of two protein-protein interaction networks across species. Our new IsoRank approximation exploits the mathematical properties of IsoRank’s linear system to solve the problem in quadratic time with respect to the maximum size of the two PPI networks. In experiments on synthetic and real PPI networks with various proposed metrics to measure alignment quality, we find the results of our approximate IsoRank are nearly as accurate as the original IsoRank. And for functional enrichment-based measures of global network alignment quality we find our approximation performs better than exact IsoRank, doubtless because it is more robust to the noise of missing or incorrect edges. Second, we describe our new ILP-based method named GIDEON to search for a diverse collection of Between-Pathway Models (BPMs) in the Yeast genetic interaction network, where the genetic interaction network is a weighted signed graph representation of a series of high-throughput pairwise epistasis experiments. More specifically: the vertices of the genetic interaction network represent non-essential genes, and two genes are connected with a positive (or negative) weighted edge when the yeast strain of the double knockout is more healthy (or sicker) than would be expected by examining the sickness of its component single knockout strains. In this network, BPMs are a graph motif signature that indicates potential compensatory pathways. We discuss both the novel ILP formulation as well as potential biological applications. Finally, D-SCRIPT is a powerful lightweight deep learning method designed for high-throughput inference of protein–protein interactions (PPIs) using a pre-trained protein language model, but it is expensive in time and memory to infer all PPIs for network-/proteome-level analyses. We introduce D-SCRIPT with blocked multi-GPU parallel inference, which substantially reduces memory usage across tasks and computational systems ( for a representative large proteome) and enables multi-GPU parallelism.