Randomized algorithms
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
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Design networks with bounded pairwise distance
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
A constant-factor approximation algorithm for the k-MST problem
Journal of Computer and System Sciences
A polylogarithmic approximation algorithm for the group Steiner tree problem
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
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
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximating a Finite Metric by a Small Number of Tree Metrics
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Approximation algorithms for the covering Steiner problem
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
On the approximability of some network design problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A Recursive Greedy Algorithm for Walks in Directed Graphs
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A near-tight approximation lower bound and algorithm for the kidnapped robot problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A greedy approximation algorithm for the group Steiner problem
Discrete Applied Mathematics
On the approximability of some network design problems
ACM Transactions on Algorithms (TALG)
A greedy approximation algorithm for the group Steiner problem
Discrete Applied Mathematics
On a class of branching problems in broadcasting and distribution
Computers and Operations Research
The polymatroid steiner problems
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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Network design problems, such as generalizations of the Steiner Tree Problem, can be cast as edge-cost-flow problems (a.k.a. fixed-charge flows). We prove a hardness result for the Minimum Edge Cost Flow Problem (MECF). Using the one-round two-prover scenario, we prove that MECF in directed graphs does not admit a 2log1-驴 n-ratio approximation, for every constant 驴 0, unless NP 驴 DTIME(npolylogn) . A restricted version of MECF, called Infinite Capacity MECF (ICF), 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. We prove that directed ICF generalizes the Covering Steiner Problem. We also show that 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, where x denotes the required total flow. 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(n驴/驴5) times bigger than the cost of an optimal flow. The running time of the algorithm for directed ICF is O(x2/驴 驴 n1+1/驴). Finally, 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. This reduction can be derandomized to yield a deterministic reduction. In directed graphs, the reduction leads to a first non-trivial approximation algorithm for the Covering Steiner Problem. In undirected graphs, the resulting ratio matches the best ratio known [KRS01], via a much simpler algorithm.