Abstract
We consider the directed Rooted Subset k -Edge-Connectivity problem: given a digraph \(G=(V,E)\) with edge costs, a set \(T \subset V\) of terminals, a root node r, and an integer k, find a min-cost subgraph of G that contains k edge disjoint rt-paths for all \(t \in T\). The case when every edge of positive cost has head in T admits a polynomial time algorithm due to Frank [9], and the case when all positive cost edges are incident to r is equivalent to the k -Multicover problem. Recently, Chan et al. [2] obtained ratio \(O(\ln k \ln |T|)\) for quasi-bipartite instances, when every edge in G has an end (tail and/or head) in \(T+r\). We give a simple proof for the same ratio for a more general problem of covering an arbitrary T-intersecting supermodular set function by a minimum cost edge set, and for the case when only every positive cost edge has an end in \(T+r\).
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Nutov, Z. (2021). On Rooted k-Connectivity Problems in Quasi-bipartite Digraphs. In: Santhanam, R., Musatov, D. (eds) Computer Science – Theory and Applications. CSR 2021. Lecture Notes in Computer Science(), vol 12730. Springer, Cham. https://doi.org/10.1007/978-3-030-79416-3_20
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