Network Alignment - Erciyes, Kayhan (Distributed and Sequential Algorithms for Bioinformatics, 2015)
Biological networks are dynamic and the measurements can contain errors which results in two networks of the same origin to look different. Alignment of two or more networks is the process of searching for similarities between them. This task requires mapping nodes of one network to another by associating some similarity measure with the aim of pairing nodes that have the highest affinity. Network alignment is needed to compare biological networks to find their phylogenetic relationships and to find approximately conserved subnetworks in them. Since this problem is intractable, various heuristic algorithms are proposed. In the graph domain, the alignment operation can be accomplished by forming a weighted complete k-partite graph with partitions from each network and edge weights showing the similarity. The problem is then reduced to maximal weighted complete k-partite matching problem which has been investigated thoroughly. In this chapter, we first state the relation of the problem to graph isomorphism and the weighted complete k-partite matching and show the metrics for the alignment quality. We then review few sequential algorithms for this problem. Distributed alignment algorithms are scarce and we propose a new algorithm that uses k-partite matching property.