Graph orientation is a fundamental problem in graph theory that has recently arisen in the study of signaling-regulatory pathways in protein networks. Given a graph and a list of ordered source-target vertex pairs, it calls for assigning directions to the edges of the graph so as to maximize the number of pairs that admit a directed source-to-target path. When the input graph is undirected, a sub-logarithmic approximation is known for the problem. However, the approximability of the biologically-relevant variant, in which the input graph has both directed and undirected edges, was left open. Here we give the first approximation algorithm to this problem. Our algorithm provides a sub-linear guarantee in the general case, and logarithmic guarantees for structured instances. © 2011 Springer-Verlag.
CITATION STYLE
Elberfeld, M., Segev, D., Davidson, C. R., Silverbush, D., & Sharan, R. (2011). Approximation algorithms for orienting mixed graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6661 LNCS, pp. 416–428). https://doi.org/10.1007/978-3-642-21458-5_35
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