The explosive growth of cellular network databases requires novel analytical methods constituting a new interdisciplinary area of computational systems biology. The main problems in this area are finding conserved subnetworks, integrating interacting gene networks, protein networks, and biochemical reactions, discovering critical elements or modules, and finding homologous pathways. With the immense increase in good-quality data from high throughput genomic and proteomic technologies, studies of these questions are becoming more and more challenging from analytical and computational perspectives.
This chapter deals with network mappings, a central tool for comparing and exploring biological networks. When mapping metabolic pathways by matching similar enzymes and chemical reaction chains, one can match homologous pathways. Network mapping can be used for predicting unknown pathways, fast and meaningful searching of databases, and potentially establishing evolutionary relations. This tool integrated with protein database search can be used for filling pathway holes.
Let the pattern be a pathway for which one is searching for homologous pathways in the text such as the known metabolic network of a different species. Existing mapping tools on this problem are mostly based on isomorphic and homeomorphic embeddings (see [31–43] and [3–14, 16]), effectively solving a problem that is NP-complete  even when searching a match for a tree in acyclic networks.
Given a ...