TY - JOUR

T1 - Erratum

T2 - Approximating minimum-cost connectivity problems via uncrossable bifamilies (ACM Transactions on Algorithms (2012) 9:1 (1) DOI: 10.1145/2390176.2390177)

AU - Nutov, Zeev

N1 - Publisher Copyright:
© 2018 ACM.

PY - 2018/7

Y1 - 2018/7

N2 - 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) Survivable Network problem. The input consists of a graph G = (V, E) with edge-costs, a set T ⊆ V of terminals, and connectivity demands {rst > 0: st ∈ D ⊆ T × T}. The goal is to find a minimum cost subgraph of G that for all st ∈ D contains rst 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 = maxst ∈D rst is the maximum demand. This ratio is correct when the requirements are rst = k for all t ∈ T \ {s}, but for general rooted demands our article implies only ratio O(k2) (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.

AB - 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) Survivable Network problem. The input consists of a graph G = (V, E) with edge-costs, a set T ⊆ V of terminals, and connectivity demands {rst > 0: st ∈ D ⊆ T × T}. The goal is to find a minimum cost subgraph of G that for all st ∈ D contains rst 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 = maxst ∈D rst is the maximum demand. This ratio is correct when the requirements are rst = k for all t ∈ T \ {s}, but for general rooted demands our article implies only ratio O(k2) (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.

UR - http://www.scopus.com/inward/record.url?scp=85052002503&partnerID=8YFLogxK

U2 - 10.1145/3186991

DO - 10.1145/3186991

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.comment???

AN - SCOPUS:85052002503

SN - 1549-6325

VL - 14

JO - ACM Transactions on Algorithms

JF - ACM Transactions on Algorithms

IS - 3

M1 - 37

ER -