Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
Randomized algorithms
Chernoff-Hoeffding Bounds for Applications with Limited Independence
SIAM Journal on Discrete Mathematics
An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm
SIAM Journal on Computing
Bicriteria network design problems
Journal of Algorithms
A polylogarithmic approximation algorithm for the group Steiner tree problem
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Provisioning a virtual private network: a network design problem for multicommodity flow
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Algorithms for provisioning virtual private networks in the hose model
Proceedings of the 2001 conference on Applications, technologies, architectures, and protocols for computer communications
Introduction to algorithms
Approximation algorithms for the covering Steiner problem
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
On the Single-Source Unsplittable Flow Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Fairness in Routing and Load Balancing
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
How good can IP routing be?
Single-source unsplittable flow
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Bounded branching process and and/or tree evaluation
Random Structures & Algorithms
Theory of communication networks
Algorithms and theory of computation handbook
Capacitated confluent flows: complexity and algorithms
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Polynomial-time algorithms for special cases of the maximum confluent flow problem
Discrete Applied Mathematics
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In this paper, we investigate the problem of determining confluent flows with minimum congestion. A flow of a given commodity is said to be confluent if at any node all the flow of the commodity departs along a single edge. Confluent flows appear in a variety of application areas ranging from wireless communications to evacuations; in fact, most flows in the Internet are confluent since Internet routing is destination based. We consider the single-commodity confluent flow problem, in which we are given an n-node directed network G, a sink t and supplies at each node, and the goal is to find a confluent flow that routes all the supplies to the sink while minimizing the maximum edge congestion. Our main result is an approximation algorithm, based on randomized rounding, for the special case when all the supplies are uniform; the algorithm finds a confluent flow with edge (and node) congestion O(C^2log^3n), where C is the node congestion of a splittable flow with minimum node congestion; here the node congestion of a flow is the maximum, over all nodes other than t, of the congestion at a node. This implies an O@?(n) approximation algorithm for the problem with uniform supplies. Our result relies on the analysis of a natural probabilistic process defined on directed acyclic graphs, that may be of independent interest. For tree networks, we present an optimal polynomial-time algorithm for a multi-sink generalization of the above confluent flow problem. We show that it is NP-hard to approximate the congestion of the optimal confluent flow for general networks to within a factor of 32. We also establish a lower bound on the gap between confluent and splittable flows, and consider multi-commodity and fractional versions of confluent flow problems.