Erratum

Abstract

There are two errors in our article “Approximating Minimum-Cost Connectivity Problems via Uncrossable Bifamilies” ( ACM Transactions on Algorithms ( TALG ), 9(1), Article No. 1, 2012). In that article, we consider the (undirected) S URVIVABLE N ETWORK problem. The input consists of a graph G =( V , E ) with edge-costs, a set T ⊆ V of terminals, and connectivity demands { r st > 0 : st ∈ D ⊆ T × T } . The goal is to find a minimum cost subgraph of G that for all st ∈ D contains r st pairwise internally disjoint st -paths. We claimed ratios O ( k ln k ) for rooted demands when the set D of demand pairs form a star, where k = max st ∈ D r st is the maximum demand. This ratio is correct when the requirements are r st = k for all t ∈ T \{ s }, but for general rooted demands our article implies only ratio O ( k 2 ) (which, however, is still the currently best-known ratio for the problem). We also obtained various ratios for the node-weighted version of the problem. These results are valid, but the proof needs a correction described here.