Optimal oblivious routing in polynomial time
@article{Azar2003OptimalOR,
title={Optimal oblivious routing in polynomial time},
author={Yossi Azar and Edith Cohen and Amos Fiat and Haim Kaplan and Harald R{\"a}cke},
journal={J. Comput. Syst. Sci.},
year={2003},
volume={69},
pages={383-394},
url={https://api.semanticscholar.org/CorpusID:33364366}
}This work gives a polynomial time construction that guarantees Racke's bounds, and more generally gives the true optimal ratio for any network.
3,373 Citations
Compact Oblivious Routing
- 2019
Computer Science
This paper presents the first oblivious routing scheme which guarantees close to optimal load and is compact at the same time -- requiring routing tables of polylogarithmic size.
A practical algorithm for constructing oblivious routing schemes
- 2003
Computer Science
This paper presents a combinatorial algorithm for constructing an oblivious routing scheme that guarantees a competitive ratio of O(log4n) for undirected networks and yields a proof for the existence of an oblivious routed scheme with competitive ratio O( log3n), which is much simpler than the original proof.
New lower bounds for oblivious routing in undirected graphs
- 2006
Computer Science, Mathematics
A natural candidate model for evaluating the throughput of an oblivious routing scheme which subsumes all suggested models for the throughputof oblivious routing considered so far and proves a lower bound Ω(log n/log log n) for the competitive ratio of any oblivious routing schemes.
Oblivious routing in directed graphs with random demands
- 2005
Computer Science
This work shows that Räcke showed that there is an oblivious routing algorithm with polylogarithmic competitive ratio (w.r.t. edge congestion) for any undirected graph, and presents the first oblivious routing algorithms which is O(log2 n) competitive with high probability in directed graphs given that the demands are chosen randomly from a known demand-distribution.
On a New Competitive Measure for Oblivious Routing
- 2014
Computer Science
A general lower bound on the volumetric ratio is shown, and the competitivity of oblivious routing in terms of the new measure quickly vanishes even in relatively small common-place topologies.
On the Competitiveness of Oblivious Routing: A Statistical View
- 2021
Computer Science, Mathematics
The main result is the finding that, in certain directed graphs on n nodes, the probability of congestion approaches 1 in some undirected graphs, despite the competitive ratio being O(1).
Oblivious routing on node-capacitated and directed graphs
- 2007
Computer Science, Mathematics
It is shown that 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, and it is settled an open question about routing problems in which all commodities share a common source or sink.
Online oblivious routing
- 2003
Computer Science
An algorithm is presented that achieves a competitive ratio arbitrarily to close to that of Azar et al [4], while at the same time performing nearly as well as the optimal static routing for the given sequence of demands.
Minimizing average latency in oblivious routing
- 2008
Computer Science
This work considers the problem of minimizing average latency cost while obliviously routing traffic in a network with linear latency functions and shows that for the case when all routing requests are directed to a single target, there is a routing scheme with competitive ratio O(log n), where n denotes the number of nodes in the network.
Semi-oblivious routing: lower bounds
- 2007
Computer Science
The 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).
17 References
Tight bounds for oblivious routing in the hypercube
- 1990
Computer Science, Mathematics
We prove that in anyN-node communication network with maximum degreed, any deterministic oblivious algorithm for routing an arbitrary permutation requires Ω(√N/d) parallel communication steps in the…
A practical algorithm for constructing oblivious routing schemes
- 2003
Computer Science
This paper presents a combinatorial algorithm for constructing an oblivious routing scheme that guarantees a competitive ratio of O(log4n) for undirected networks and yields a proof for the existence of an oblivious routed scheme with competitive ratio O( log3n), which is much simpler than the original proof.
Online oblivious routing
- 2003
Computer Science
An algorithm is presented that achieves a competitive ratio arbitrarily to close to that of Azar et al [4], while at the same time performing nearly as well as the optimal static routing for the given sequence of demands.
A polynomial-time tree decomposition to minimize congestion
- 2003
Computer Science, Mathematics
How to compute a hierarchical decomposition and a corresponding oblivious routing strategy in polynomial time is shown and the decomposition gives an improved competitive ratio for congestion of O(log2 n log log n).
Universal schemes for parallel communication
- 1981
Computer Science
This paper shows that there exists an N-processor computer that can simulate arbitrary N- processor parallel computations with only a factor of O(log N) loss of runtime efficiency, and isolates a combinatorial problem that lies at the heart of this question.
Randomized rounding: A technique for provably good algorithms and algorithmic proofs
- 1987
Mathematics, Computer Science
A randomized algorithm for transforming an optimal solution of a relaxed problem into a provably good solution for the 0–1 problem is given and can be extended to provide bounds on the disparity between the rational and 0-1 optima for a given problem instance.
Minimizing Congestion in General Networks
- 2002
Computer Science, Engineering
This work introduces a framework for solving online problems that aim to minimize the congestion in general topology networks and achieves a competitive ratio of O(log/sup 3/ n) with respect to the congestion of the network links.
On-line Network Routing
- 1996
Computer Science, Engineering
This chapter has concentrated on routing in electrical and optical networks, presented algorithms for load minimization and throughput maximization problems, and mentioned some of the most popular open problems in the area.
Routing, merging and sorting on parallel models of computation
- 1982
Computer Science
It is shown that log log n - log log r is asymptotically optimal for rn processors to merge two sorted lists of n elements and is able to achieve such an efficient sort via Valiant's parallel merging algorithm.