We consider the directed Rooted Subset k -Edge-Connectivity problem: given a digraph G= (V, E) with edge costs, a set T⊂ 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∈ T. The case when every edge of positive cost has head in T admits a polynomial time algorithm due to Frank , and the case when all positive cost edges are incident to r is equivalent to the k -Multicover problem. Recently, Chan et al.  obtained ratio O(ln kln | 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.
|Title of host publication||Computer Science – Theory and Applications - 16th International Computer Science Symposium in Russia, CSR 2021, Proceedings|
|Editors||Rahul Santhanam, Daniil Musatov|
|Publisher||Springer Science and Business Media Deutschland GmbH|
|Number of pages||10|
|State||Published - 2021|
|Event||16th International Computer Science Symposium in Russia, CSR 2021 - Sochi, Russian Federation|
Duration: 28 Jun 2021 → 2 Jul 2021
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||16th International Computer Science Symposium in Russia, CSR 2021|
|Period||28/06/21 → 2/07/21|
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