Provably good routing in graphs: regular arrays
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Approximations for the disjoint paths problem in high-diameter planar networks
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Decision algorithms for unsplittable flow and the half-disjoint paths problem
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Online computation and competitive analysis
Online computation and competitive analysis
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Approximation Algorithms for Disjoint Paths and Related Routing and Packing Problems
Mathematics of Operations Research
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
Approximation algorithms for disjoint paths problems
Approximation algorithms for disjoint paths problems
Throughput-competitive on-line routing
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Call Control with k Rejections
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Approximation Algorithms for the Unsplittable Flow Problem
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Hardness of the Undirected Edge-Disjoint Paths Problem with Congestion
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Greedy approximation via duality for packing, combinatorial auctions and routing
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
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
Throughput and energy-aware routing for 802.11 based mesh networks
Computer Communications
Approximation Techniques for Utilitarian Mechanism Design
SIAM Journal on Computing
A logarithmic approximation for unsplittable flow on line graphs
ACM Transactions on Algorithms (TALG)
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We provide the first strongly polynomial algorithms with the best approximation ratio for all three variants of the unsplittable flow problem (UFP). In this problem we are given a (possibly directed) capacitated graph with n vertices and m edges, and a set of terminal pairs each with its own demand and profit. The objective is to connect a subset of the terminal pairs each by a single flow path as to maximize the total profit of the satisfied terminal pairs subject to the capacity constraints. Classical UFP, in which demands must be lower than edge capacities, is known to have an O(√m) approximation algorithm. We provide the same result with a strongly polynomial combinatorial algorithm. The extended UFP case is when some demands might be higher than edge capacities. For that case we both improve the current best approximation ratio and use strongly polynomial algorithms. We also use a lower bound to show that the extended case is provably harder than the classical case. The last variant is the bounded UFP where demands are at most 1/K of the minimum edge capacity. Using strongly polynomial algorithms here as well, we improve the currently best known algorithms. Specifically, for K = 2 our results are better than the lower bound for classical UFP thereby separating the two problems.