An approximation algorithm for the generalized assignment problem
Mathematical Programming: Series A and B
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms for Single-Source Unsplittable Flow
SIAM Journal on Computing
On the k-Splittable Flow Problem
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Single-source unsplittable flow
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
Single-source k-splittable min-cost flows
Operations Research Letters
A Branch and Price algorithm for the k-splittable maximum flow problem
Discrete Optimization
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In the single-source unsplittable flow problem, commodities must be routed simultaneously from a common source vertex to certain sinks in a given directed graph with edge capacities and costs. The demand of each commodity must be routed along a single path so that the total flow through any edge is at most its capacity. Moreover the cost of the solution should not exceed a given budget. An important open question is whether a simultaneous (2,1)-approximation can be achieved for minimizing congestion and cost, i.e., the budget constraint should not be violated. In this note we show that this is possible for the case of 2-splittable flows, i.e., flows where the demand of each commodity is routed along at most two paths. Our result holds under the ''no-bottleneck'' assumption, i.e., the maximum demand does not exceed the minimum capacity.