Minimum augmentation to k-edge-connect specified vertices of a graph
The k-edge-connectivity augmentation problem for a specified set of vertices (kECA-SV for short) is defined by “Given a graph G=(V, E) and a subset Γ\(\subseteq \)V, find a minimum set E′ of edges,each connecting distinct vertices of V, such that G′=(V, E ∪ E′) has at least k edge-disjoint paths between any pair of vertices in Γ”. We propose an O(λ2¦V¦(¦V¦+¦Γ¦log λ)+¦E¦) algorithm for (λ + 1)ECA-SV with Γ(V), where λ is the edge-connectivity of Γ (the cardinality of a minimum cut separating two vertices of Γ). Also mentioned is an O(¦V¦ log ¦V¦+¦E¦) algorithm for a special case where λ is equal to the edge-connectivity of G.
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