Existence and Construction of Edge-Disjoint Pathson Expander Graphs
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
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
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
Oblivious routing on node-capacitated and directed graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Distributed online call control on general networks
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Finding effective support-tree preconditioners
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Route planning under uncertainty: the Canadian traveller problem
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 2
Oblivious routing in fat-tree based system area networks with uncertain traffic demands
IEEE/ACM Transactions on Networking (TON)
Electric Routing and Concurrent Flow Cutting
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
TOLB: a traffic-oblivious load-balancing protocol for next-generation sensornets
ADHOC-NOW'07 Proceedings of the 6th international conference on Ad-hoc, mobile and wireless networks
Electric routing and concurrent flow cutting
Theoretical Computer Science
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Oblivious routing algorithms for general undirected networks were introduced by Räcke, and this work has led to many subsequent improvements and applications. Räcke showed that there is an oblivious routing algorithm with polylogarithmic competitive ratio (with respect to edge congestion) for any undirected graph. However, there are directed networks for which the competitive ratio is in Ω(√n).To cope with this inherent hardness in general directed networks, the concept of oblivious routing with demands chosen randomly from a known demand distribution was introduced recently. Under this new model, O(log2 n)-competitiveness with high probability is possible in general directed graphs.However, it remained an open problem whether or not the competitive ratio, under this new model, could also be significantly improved in undirected graphs. In this paper, we rule out this possibility by providing a lower bound of Ω(log n/log log n) for the multicommodity case and Ω(√logn) for the single-sink case for oblivious routing in a random demand model.We also introduce a natural candidate model for evaluating the throughput of an oblivious routing scheme which subsumes all suggested models for the throughput of oblivious routing considered so far. In this general model, we first prove a lower bound Ω(log n/log log n) for the competitive ratio of any oblivious routing scheme. Interestingly, the graphs that we consider for the lower bound in this case are expanders, for which we also obtain a lower bound Ω(log n/log log n) on the competitive ratio of congestion based oblivious routing with adversarial demands.