Inferring (Biological) Signal Transduction Networks via Transitive Reductions of Directed Graphs
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The minimum equivalent digraph problem, that correspond to a special case of TR1 with no critical edges, is known to be MAX-SNP-hard, admits a polynomial time algorithm with an approximation ratio of 1.617+ε for any constant ε>0 (Chiu and Liu in Sci. Sin. 4:1396–1400, 1965) and can be solved in linear time for directed acyclic graphs (Aho et al. in SIAM J. Comput. 1(2):131–137, 1972).
We observe that TR p , for any integer p>0, can be solved in linear time for directed acyclic graphs using the ideas in Aho et al. (SIAM J. Comput. 1(2):131–137, 1972).
We provide a 1.78-approximation for TR1 that improves the 2-approximation mentioned in (2) above.
We provide a 2+o(1)-approximation for TR p on general graphs for any fixed prime p>1.
KeywordsTransitive reduction of directed graphs Minimum equivalent digraph (Biological) signal transduction networks Approximation algorithms
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