Abstract
Given a directed graphG, acovering is a subsetB of edges which meets all directed cuts ofG. Equivalently, the contraction of the elements ofB makesG strongly connected. AnO(n 5) primal-dual algorithm is presented for finding a minimum weight covering of an edge-weighted digraph. The algorithm also provides a constructive proof for a min-max theorem due to Lucchesi and Younger and for its weighted version.
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Frank, A. How to make a digraph strongly connected. Combinatorica 1, 145–153 (1981). https://doi.org/10.1007/BF02579270
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DOI: https://doi.org/10.1007/BF02579270