SANA: Simulated Annealing Network Alignment Applied to Biological Networks

The alignment of biological networks has the potential to teach us as much about biology and disease as has sequence alignment. Sequence alignment can be optimally solved in polynomial time. In contrast, network alignment is $NP$-hard, meaning optimal solutions are impossible to find, and the quality of found alignments depend strongly upon the algorithm used to create them. Every network alignment algorithm consists of two orthogonal components: first, an objective function or measure $M$ that is used to evaluate the quality of any proposed alignment, and second, a search algorithm used to explore the exponentially large set of possible alignments in an effort to find "good" ones according to $M$. Objective functions fall into many categories, including biological measures such as sequence similarity, as well as topological measures like graphlet similarity and edge coverage (possibly weighted). Algorithms to search the space of all possible alignments can be deterministic or stochastic, and many possibilities have been offered over the past decade. In this paper we introduce a new stochastic search algorithm called SANA: Simulated Annealing Network Aligner. We test it on several popular objective functions and demonstrate that it almost universally optimizes each one significantly better than existing search algorithms. Finally, we compare several topological objective functions using SANA. Software available at http://sana.ics.uci.edu.