A matroid approach to finding edge connectivity and packing arborescences
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
On strongly connected digraphs with bounded cycle length
Discrete Applied Mathematics
Approximating the minimum equivalent digraph
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Approximating the minimum strongly connected subgraph via a matching lower bound
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Approximating Minimum-Size k-Connected Spanning Subgraphs via Matching
SIAM Journal on Computing
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
A linear time 5/3-approximation for the minimum strongly-connected spanning subgraph problem
Information Processing Letters
Special edges, and approximating the smallest directed k-edge connected spanning subgraph
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
On the Integrality Ratio for the Asymmetric Traveling Salesman Problem
Mathematics of Operations Research
Iterated rounding algorithms for the smallest k-edge connected spanning subgraph
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
An O(log n/ log log n)-approximation algorithm for the asymmetric traveling salesman problem
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A Randomized Rounding Approach to the Traveling Salesman Problem
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Online stochastic matching: online actions based on offline statistics
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Improving christofides' algorithm for the s-t path TSP
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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In the k-arc connected subgraph problem, we are given a directed graph G and an integer k and the goal is the find a subgraph of minimum cost such that there are at least k-arc disjoint paths between any pair of vertices. We give a simple (1+1/k)-approximation to the unweighted variant of the problem, where all arcs of G have the same cost. This improves on the 1+2/k approximation of Gabow et al. [GGTW09]. Similar to the 2-approximation algorithm for this problem [FJ81], our algorithm simply takes the union of a k in-arborescence and a k out-arborescence. The main difference is in the selection of the two arborescences. Here, inspired by the recent applications of the rounding by sampling method (see e.g. [AGM+10, MOS11, OSS11, AKS12]), we select the arborescences randomly by sampling from a distribution on unions of k arborescences that is defined based on an extreme point solution of the linear programming relaxation of the problem. In the analysis, we crucially utilize the sparsity property of the extreme point solution to upper-bound the size of the union of the sampled arborescences. To complement the algorithm, we also show that the integrality gap of the minimum cost strongly connected subgraph problem (i.e., when k=1) is at least 3/2−ε, for any ε0. Our integrality gap instance is inspired by the integrality gap example of the asymmetric traveling salesman problem [CGK06], hence providing further evidence of connections between the approximability of the two problems.