Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
Probabilistic construction of deterministic algorithms: approximating packing integer programs
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
The steiner problem with edge lengths 1 and 2,
Information Processing Letters
Fast approximation algorithms for fractional packing and covering problems
Mathematics of Operations Research
Coordination complexity of parallel price-directive decomposition
Mathematics of Operations Research
Randomized rounding without solving the linear program
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Randomized metarounding (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
IEEE/ACM Transactions on Networking (TON)
Towards a Practical Volumetric Cutting Plane Method for Convex Programming
SIAM Journal on Optimization
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating Multicast Congestion
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
Approximation Algorithms for General Packing Problems with Modified Logarithmic Potential Function
TCS '02 Proceedings of the IFIP 17th World Computer Congress - TC1 Stream / 2nd IFIP International Conference on Theoretical Computer Science: Foundations of Information Technology in the Era of Networking and Mobile Computing
Faster and Simpler Algorithms for Multicommodity Flow and other Fractional Packing Problems.
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Minimum k Arborescences with Bandwidth Constraints
Algorithmica
An Approximate Max-Steiner-Tree-Packing Min-Steiner-Cut Theorem
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Implementation of approximation algorithms for the multicast congestion problem
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Research: A group multicast routing algorithm by using multiple minimum Steiner trees
Computer Communications
On routing in VLSI design and communication networks
Discrete Applied Mathematics
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Given an undirected edge-capacitated graph and a collection of subsets of vertices, we consider the problem of selecting a maximum (weighted) set of Steiner trees, each spanning a given subset of vertices without violating the capacity constraints. We give an integer linear programming (ILP) formulation, and observe that its linear programming (LP-) relaxation is a fractional packing problem with exponentially many variables and with a block (sub-)problem that cannot be solved in polynomial time. To this end, we take an r-approximate block solver to develop a (1−ε)/r approximation algorithm for the LP-relaxation. The algorithm has a polynomial coordination complexity for any ε∈(0,1). To the best of our knowledge, this is the first approximation result for fractional packing problems with only approximate block solvers and a coordination complexity that is polynomial in the input size and ε−1. This leads to an approximation algorithm for the underlying tree packing problem. Finally, we extend our results to an important multicast routing and wavelength assignment problem in optical networks, where each Steiner tree is also to be assigned one of a limited set of given wavelengths, so that trees crossing the same fiber are assigned different wavelengths.