Lagrangian Relaxation Applied to Sparse Global Network Alignment
Data on molecular interactions is increasing at a tremendous pace, while the development of solid methods for analyzing this network data is lagging behind. This holds in particular for the field of comparative network analysis, where one wants to identify commonalities between biological networks. Since biological functionality primarily operates at the network level, there is a clear need for topology-aware comparison methods. In this paper we present a method for global network alignment that is fast and robust, and can flexibly deal with various scoring schemes taking both node-to-node correspondences as well as network topologies into account. It is based on an integer linear programming formulation, generalizing the well-studied quadratic assignment problem. We obtain strong upper and lower bounds for the problem by improving a Lagrangian relaxation approach and introduce the software tool natalie 2.0, a publicly available implementation of our method. In an extensive computational study on protein interaction networks for six different species, we find that our new method outperforms alternative state-of-the-art methods with respect to quality and running time. An extended version of this paper including proofs and pseudo code is available at http://arxiv.org/pdf/1108.4358v1 .
KeywordsInteger Linear Programming Protein Protein Interaction Network Quadratic Assignment Problem Optimal Alignment Integer Linear Programming Formulation
Unable to display preview. Download preview PDF.
- 1.Adams, W.P., Johnson, T.: Improved linear programming-based lower bounds for the quadratic assignment problem. DIMACS Series in Discrete Mathematics and Theoretical Computer Science (1994)Google Scholar
- 3.Ashburner, M., Ball, C.A., Blake, J.A., et al.: Gene ontology: tool for the unification of biology. Nat. Genet. 25 (2000)Google Scholar
- 13.Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum Press (1972)Google Scholar
- 25.Wohlers, I., Andonov, R., Klau, G.W.: Algorithm engineering for optimal alignment of protein structure distance matrices. Optim. Lett. (2011)Google Scholar