The point-to-point delivery and connection problems: complexity and algorithms
Discrete Applied Mathematics
A set covering reformulation of the pure fixed charge transportation problem
CO89 Selected papers of the conference on Combinatorial Optimization
When Trees Collide: An Approximation Algorithm for theGeneralized Steiner Problem on Networks
SIAM Journal on Computing
Randomized algorithms
Spanning Trees---Short or Small
SIAM Journal on Discrete Mathematics
The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
SIAM Journal on Computing
A constant-factor approximation algorithm for the k-MST problem
Journal of Computer and System Sciences
Approximating the weight of shallow Steiner trees
Discrete Applied Mathematics
Approximation algorithms for directed Steiner problems
Journal of Algorithms
An approximation algorithm for the covering Steiner problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A polylogarithmic approximation algorithm for the group Steiner tree problem
Journal of Algorithms
Bundle-based relaxation methods for multicommodity capacitated fixed charge network design
Discrete Applied Mathematics - Special issue on the combinatorial optimization symposium
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximation algorithms for the covering Steiner problem
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
On the Hardness of Approximation Spanners
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
Approximating a Finite Metric by a Small Number of Tree Metrics
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
A 3-approximation for the minimum tree spanning k vertices
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
A solution approach to the fixed charge network flow problem using a dynamic slope scaling procedure
Operations Research Letters
Optimal positioning of active and passive monitoring devices
CoNEXT '05 Proceedings of the 2005 ACM conference on Emerging network experiment and technology
Design of IEEE 802.16-based multi-hop wireless backhaul networks
AcessNets '06 Proceedings of the 1st international conference on Access networks
Terminal backup, 3D matching, and covering cubic graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Combinatorial optimization in system configuration design
Automation and Remote Control
Approximating k-generalized connectivity via collapsing HSTs
Journal of Combinatorial Optimization
Finding paths with minimum shared edges
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Terminal Backup, 3D Matching, and Covering Cubic Graphs
SIAM Journal on Computing
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Finding paths with minimum shared edges
Journal of Combinatorial Optimization
A Survey of Parallel and Distributed Algorithms for the Steiner Tree Problem
International Journal of Parallel Programming
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Network design problems, such as generalizations of the Steiner Tree Problem, can be cast as edge-cost-flow problems. An edge-cost flow problem is a min-cost flow problem in which the cost of the flow equals the sum of the costs of the edges carrying positive flow.We prove a hardness result for the Minimum Edge Cost Flow Problem (MECF). Using the one-round two-prover scenario, we prove that MECF does not admit a 2log1-ϵ n-ratio approximation, for every constant ϵ 0, unless NP ⊆ DTIME(npolylogn).A restricted version of MECF, called Infinite Capacity MECF (ICF), is defined. The ICF problem is defined as follows: (i) all edges have infinite capacity, (ii) there are multiple sources and sinks, where flow can be delivered from every source to every sink, (iii) each source and sink has a supply amount and demand amount, respectively, and (iv) the required total flow is given as part of the input. The goal is to find a minimum edge-cost flow that meets the required total flow while obeying the demands of the sinks and the supplies of the sources. This problem naturally arises in practical scheduling applications, and is equivalent to the special case of single source MECF, with all edges not touching the source or the sink having infinite capacity.The directed ICF generalizes the Covering Steiner Problem in directed and undirected graphs. The undirected version of ICF generalizes several network design problems, such as: Steiner Tree Problem, k-MST, Point-to-point Connection Problem, and the generalized Steiner Tree Problem.An O(log x)-approximation algorithm for undirected ICF is presented. We also present a bi-criteria approximation algorithm for directed ICF. The algorithm for directed ICF finds a flow that delivers half the required flow at a cost that is at most O(nϵ/ϵ4) times bigger than the cost of an optimal flow. The running time of the algorithm is O(x2/ϵ ċ n1+1/ϵ), where x denotes the required total flow.Randomized approximation algorithms for the Covering Steiner Problem in directed and undirected graphs are presented. The algorithms are based on a randomized reduction to a problem called 1/2-Group Steiner. In undirected graphs, the approximation ratio matches the approximation ratio of Konjevod et al. [2002]. However, our algorithm is much simpler. In directed graphs, the algorithm is the first nontrivial approximation algorithm for the Covering Steiner Problem. Deterministic algorithms are obtained by derandomization.