Parameterized Complexity of Arc-Weighted Directed Steiner Problems
Jiong Guo, Rolf Niedermeier, Ondřej Suchý · SIAM Journal on Discrete Mathematics · 2011
We start a systematic parameterized computational complexity study of three NP-hard network design problems on arc-weighted directed graphs: directed Steiner tree, strongly connected Steiner subgraph, and directed Steiner network. We investigate their parameterized complexities with respect to the three parameterizations: “number of terminals,” “an upper bound on the size of the connecting network,” and the combination of these two. We achieve several parameterized hardness results as well as some fixed-parameter tractability results, in this way extending previous results of Feldman and Ruhl [SIAM J. Comput., 36 (2006), pp. 543–561].