TY - GEN

T1 - Improved approximating algorithms for Directed Steiner Forest

AU - Feldman, Moran

AU - Kortsarz, Guy

AU - Nutov, Zeev

PY - 2009

Y1 - 2009

N2 - We consider the k-Directed Steiner Forest (k-DSF) problem: given a directed graph G = (V, E) with edge costs, a collection D ⊆ V x V of ordered node pairs, and an integer k ≤ |D|, find a min-cost subgraph H of G that contains an st-path for (at least) kc pairs (s, t) ∈ D. When k = |D|, we get the Directed Steiner Forest (DSF) problem. The best known approximation ratios for these problems are: Õ(k 2/3) for k-DSF by Charikar et al. [2], and O(k 1/2+ε) for DSF by Chekuri et al. [3]. For DSF we give an O(n ε·mm{n 4/5, m 2/3})-approximation scheme using a novel LP-relaxation seeking to connect pairs via "cheap" paths. This is the first sublinear (in terms of n = |V|) approximation ratio for the problem. For k-DSF we give a simple greedy O(k 1/2+ε)-approximation scheme, improving the best known ratio Õ(k 2/3) by Charikar et al. [2], and (almost) matching, in terms of k, the best ratio known for the undirected variant [11]. Even when used for the particular case DSF, our algorithm favorably compares to the one of [3], which repeatedly solves linear programs, and uses complex time and space consuming transformations.

AB - We consider the k-Directed Steiner Forest (k-DSF) problem: given a directed graph G = (V, E) with edge costs, a collection D ⊆ V x V of ordered node pairs, and an integer k ≤ |D|, find a min-cost subgraph H of G that contains an st-path for (at least) kc pairs (s, t) ∈ D. When k = |D|, we get the Directed Steiner Forest (DSF) problem. The best known approximation ratios for these problems are: Õ(k 2/3) for k-DSF by Charikar et al. [2], and O(k 1/2+ε) for DSF by Chekuri et al. [3]. For DSF we give an O(n ε·mm{n 4/5, m 2/3})-approximation scheme using a novel LP-relaxation seeking to connect pairs via "cheap" paths. This is the first sublinear (in terms of n = |V|) approximation ratio for the problem. For k-DSF we give a simple greedy O(k 1/2+ε)-approximation scheme, improving the best known ratio Õ(k 2/3) by Charikar et al. [2], and (almost) matching, in terms of k, the best ratio known for the undirected variant [11]. Even when used for the particular case DSF, our algorithm favorably compares to the one of [3], which repeatedly solves linear programs, and uses complex time and space consuming transformations.

UR - http://www.scopus.com/inward/record.url?scp=70349149797&partnerID=8YFLogxK

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AN - SCOPUS:70349149797

SN - 9780898716801

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 922

EP - 931

BT - Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms

T2 - 20th Annual ACM-SIAM Symposium on Discrete Algorithms

Y2 - 4 January 2009 through 6 January 2009

ER -