STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Approximation algorithms for Steiner and directed multicuts
Journal of Algorithms
On-line routing of virtual circuits with applications to load balancing and machine scheduling
Journal of the ACM (JACM)
On-line routing in all-optical networks
Theoretical Computer Science
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
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
Multicommodity flow, well-linked terminals, and routing problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Oblivious routing in directed graphs with random demands
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Online client-server load balancing without global information
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Improved lower and upper bounds for universal TSP in planar metrics
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
New lower bounds for oblivious routing in undirected graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
ACM SIGACT News
Semi-oblivious routing: lower bounds
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for node-weighted buy-at-bulk network design
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Minimizing average latency in oblivious routing
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Node-Weighted Steiner Tree and Group Steiner Tree in Planar Graphs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Online packet admission and oblivious routing in sensor networks
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
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Oblivious routing algorithms for general undirected networks were introduced by Räcke [17], 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 non-trivial upper bounds for both these cases, providing algorithms for k-commodity oblivious routing problems with competitive ratio O(√klog(n)) for undirected node-capacitated graphs and O(√kn1/4log(n)) for directed graphs. In the special case that all commodities have a common source or sink, our upper bound becomes O(√nlog(n)) in both cases, matching the lower bound up to a factor of log(n). The lower bound (which first appeared in [6]) 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( polylog(n))competitive oblivious routing scheme for graphs of degree. For the directed case, however, we show that the lower bound of Ω(√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).