Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Approximation Algorithms for Disjoint Paths and Related Routing and Packing Problems
Mathematics of Operations Research
Simple on-line algorithms for the maximum disjoint paths problem
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Universal Routing Strategies for Interconnection Networks
Universal Routing Strategies for Interconnection Networks
SODA '03 Proceedings of the fourteenth 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
Improved Approximation Algorithms for Unsplittable Flow Problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Improved approximations for edge-disjoint paths, unsplittable flow, and related routing problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
On the Single-Source Unsplittable Flow Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Short paths in expander graphs
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Approximation algorithms for disjoint paths problems
Approximation algorithms for disjoint paths problems
A note on the greedy algorithm for the unsplittable flow problem
Information Processing Letters
Throughput-competitive on-line routing
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
A logarithmic approximation for unsplittable flow on line graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Survey on Oblivious Routing Strategies
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Unsplittable Flow in Paths and Trees and Column-Restricted Packing Integer Programs
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
ACM Transactions on Algorithms (TALG)
Oblivious low-congestion multicast routing in wireless networks
Proceedings of the thirteenth ACM international symposium on Mobile Ad Hoc Networking and Computing
Paths of bounded length and their cuts: Parameterized complexity and algorithms
Discrete Optimization
A logarithmic approximation for unsplittable flow on line graphs
ACM Transactions on Algorithms (TALG)
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In this paper we consider the unsplittable flow problem (UFP): given a directed or undirected network G=(V,E) with edge capacities and a set of terminal pairs (or requests) with associated demands, find a subset of the pairs of maximum total demand for which a single flow path can be chosen for each pair so that for every edge, the sum of the demands of the paths crossing the edge does not exceed its capacity. We present a collection of new results for the UFP both in the offline (all requests are given from the beginning) and the online (requests arrive at the system one after the other) setting. A fundamental ingredient of our analysis is the introduction of a new graph parameter, the flow number, that aims to capture global communication properties of the network. With the help of the flow number we develop a general method for transforming arbitrary multicommodity flow solutions into solutions that use short paths only. This generalizes a well-known theorem of Leighton and Rao [J. ACM 46 (6) (1999) 787-832] that applies to uniform flows only. Both the parameter and the method may therefore be of independent interest.