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
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
MPLS and traffic engineering in IP networks
IEEE Communications Magazine
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We initiate the study of semi-oblivious routing, a relaxation of oblivious routing which is first introduced by Räcke and led to many subsequent improvements and applications. In semi-oblivious routing like oblivious routing, the algorithm should select only a polynomial number of paths between the source and the sink of each commodity, but unlike oblivious routing, the flow from each source to its sink is not just a scalar multiple of the single-commodity flow; any amount of flow can be sent along each selected path. Semi-oblivious routing has several applications in traffic engineering and VLSI routing. Trivially, any competitive ratio ρ for oblivious routing (includling the polylogarthimic ratio in undirected graphs obtained by Räcke) also implies competitive ratio ρ for semi-oblivious routing. In this paper, we focus on lower bounds. We rule out the possibility of O(1) competitive ratio for semi-oblivious routing in undirected graphs by providing a lower bound of Ω(log n/log log n) in grids or even series-parallel graphs. More strongly in directed graphs, we rule out the possibility of sub-polynomial competitive ratio when the number of paths between each source and its sink is in O(n1/5). The proof of our lower bound on the grid uses a non-Markovian random walk on the integers with a mixing property which may be of independent interest. Last but not least, our lower bounds on the grid can be significantly strengthened to show that with paths of at most b bends, the competitive ratio is in Ω(n1/2b+1). This answers negatively a long-standing open problem on b-bend routing schemes in grids posed e.g. in [10, 6].