Improved Orientations of Physical Networks

The orientation of physical networks is a prime task in deciphering the signaling-regulatory circuitry of the cell. One manifestation of this computational task is as a maximum graph orientation problem, where given an undirected graph with n vertices and a collection of vertex pairs, the goal is to orient the edges of the graph so that a maximum number of pairs are connected by a directed path. We develop an approximation algorithm for this problem with a performance guarantee of O(log n/ log log n). This result improves on a previous logarithmic approximation, due to Medvedovsky et al. (WABI ’08). In addition, motivated by interactions whose direction is pre-set such as protein-DNA interactions, we extend our algorithm to handle mixed graphs, a major open problem posed by earlier work. In this setting, we demonstrate that a polylogarithmic approximation ratio is achievable under biologically-motivated assumptions on the sought paths. ∗An extended abstract of this paper appeared in Proceedings of the 10th International Workshop on Algorithms in Bioinformatics, pages 215–225, 2010. †Blavatnik School of Computer Science, Tel-Aviv University, Tel-Aviv 69978, Israel. Email: [email protected]. Supported by the Israel Science Foundation, by the European Commission under the Integrated Project QAP funded by the IST directorate as Contract Number 015848, by a European Research Council (ERC) Starting Grant, and by the Wolfson Family Charitable Trust. ‡Department of Statistics, University of Haifa, Haifa 31905, Israel. Email: [email protected]. §Blavatnik School of Computer Science, Tel-Aviv University, Tel-Aviv 69978, Israel. Email: [email protected]. Supported by a research grant from the Israel Science Foundation (grant no. 385/06).