On-line load balancing with applications to machine scheduling and virtual circuit routing
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Approximation algorithms for Steiner and directed multicuts
Journal of Algorithms
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
Minimizing Congestion in General Networks
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
On-Line Routing in All-Optical Networks
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
A practical algorithm for constructing oblivious routing schemes
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
A polynomial-time tree decomposition to minimize congestion
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Optimal oblivious routing in polynomial time
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Exploiting Locality for Data Management in Systems of Limited Bandwidth
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Universal schemes for parallel communication
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Multiway cuts in node weighted graphs
Journal of Algorithms
A general approach to online network optimization problems
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The all-or-nothing multicommodity flow problem
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Finding effective support-tree preconditioners
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
An O(n)-approximation algorithm for directed sparsest cut
Information Processing Letters
Oblivious routing in fat-tree based system area networks with uncertain traffic demands
IEEE/ACM Transactions on Networking (TON)
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Oblivious routing algorithms for general undirected networks were introduced by Räcke [2002], and this work has led to many subsequent improvements and applications. Comparatively little is known about oblivious routing in general directed networks, or even in undirected networks with node capacities. We present the first nontrivial upper bounds for both these cases, providing algorithms for k-commodity oblivious routing problems with competitive ratio O(&sqrt;k log(n)) for undirected node-capacitated graphs and O(&sqrt;k n1/4 log(n)) for directed graphs. In the special case that all commodities have a common source or sink, our upper bound becomes O(&sqrt;n log(n)) in both cases, matching the lower bound up to a factor of log(n). The lower bound (which first appeared in Azar et al. [2003]) is obtained on a graph with very high degree. We show that, in fact, the degree of a graph is a crucial parameter for node-capacitated oblivious routing in undirected graphs, by providing an O(Δ polylog(n))-competitive oblivious routing scheme for graphs of degree Δ. For the directed case, however, we show that the lower bound of Ω(&sqrt;n) still holds in low-degree graphs. Finally, we settle an open question about routing problems in which all commodities share a common source or sink. We show that even in this simplified scenario there are networks in which no oblivious routing algorithm can achieve a competitive ratio better than Ω(log n).