Static and dynamic path selection on expander graphs (preliminary version): a random walk approach
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
On-line randomized call control revisited
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
New algorithmic aspects of the Local Lemma with applications to routing and partitioning
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Edge-disjoint paths in expander graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Simple on-line algorithms for the maximum disjoint paths problem
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Improved bounds for the unsplittable flow problem
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms for the Unsplittable Flow Problem
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Disjoint Paths in Expander Graphs via Random Walks: A Short Survey
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
On Nonblocking Properties on the Benes Network
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Conductance and congestion in power law graphs
SIGMETRICS '03 Proceedings of the 2003 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
An Approximation Algorithm for the Disjoint Paths Problem in Even-Degree Planar Graphs
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
On certain connectivity properties of the internet topology
Journal of Computer and System Sciences - Special issue on FOCS 2003
Improved bounds for the unsplittable flow problem
Journal of Algorithms
Measurement and analysis of online social networks
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Minor-embedding in adiabatic quantum computation: I. The parameter setting problem
Quantum Information Processing
A logarithmic approximation for unsplittable flow on line graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Universal augmentation schemes for network navigability
Theoretical Computer Science
Minors in random regular graphs
Random Structures & Algorithms
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Testing outerplanarity of bounded degree graphs
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Edge Disjoint Paths in Moderately Connected Graphs
SIAM Journal on Computing
Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design
Quantum Information Processing
Deterministic online optical call admission revisited
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Edge disjoint paths in moderately connected graphs
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Approximation algorithms for edge-disjoint paths and unsplittable flow
Efficient Approximation and Online Algorithms
Routing in undirected graphs with constant congestion
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Random Structures & Algorithms
On the role of expander graphs in key predistribution schemes for wireless sensor networks
WEWoRC'11 Proceedings of the 4th Western European conference on Research in Cryptology
A logarithmic approximation for unsplittable flow on line graphs
ACM Transactions on Algorithms (TALG)
Adiabatic quantum programming: minor embedding with hard faults
Quantum Information Processing
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Graph expansion has proved to be a powerful general tool for analyzing the behavior of routing algorithms and the inter-connection networks on which they run. We develop new routing algorithms and structural results for bounded-degree expander graphs. Our results are unified by the fact that they are all based upon, and extend, a body of work: asserting that expanders are rich in short, disjoint paths. In particular, our work has consequences for the disjoint paths problem, multicommodity flow, and graph minor containment. We show:(i) A greedy algorithm for approximating the maximum disjoint paths problem achieves a polylogarithmic approximation ratio in bounded-degree expanders. Although our algorithm is both deterministic and on-line, its performance guarantee is an improvement over previous bounds in expanders. (ii) For a multicommodity flow problem with arbitrary demands on a bounded-degree expander there is a (1 + )-optimal solution using only flow paths of polylogarithmic length. It follows that the multicommodity flow algorithm of Awerbuch and Leighton runs in nearly linear time per commodity in expanders. Our analysis is based on establishing the following: given edge weights on an expander G, one can increase some of the weights very slightly so the resulting shortest-path metric is smooth-the min-weight path between any pair of nodes uses a polylogarithmic number of edges. (iii) Every bounded-degree expander on n nodes contains every graph with O(n/log0(1) n) nodes and edges as a minor.