A Constant Factor Approximation Algorithm for Unsplittable Flow on Paths

In this paper, we present a constant-factor approximation algorithm for the unsplittable flow problem on a path. This improves on the previous best known approximation factor of O(log n). The approximation ratio of our algorithm is 7+e for any e>;0. In the unsplittable flow problem on a path, we...

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Vydáno v:2011 IEEE 52nd Annual Symposium on Foundations of Computer Science s. 47 - 56
Hlavní autoři: Bonsma, P., Schulz, J., Wiese, A.
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: IEEE 01.10.2011
Témata:
Algorithm design and analysis
Approximation algorithms
Approximation methods
constant factor approximation
Heuristic algorithms
maximum weight independent set
Partitioning algorithms
Polynomials
resource allocation
Resource management
strong NP-hardness
unsplittable flow
ISBN:145771843X, 9781457718434
ISSN:0272-5428
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Shrnutí:In this paper, we present a constant-factor approximation algorithm for the unsplittable flow problem on a path. This improves on the previous best known approximation factor of O(log n). The approximation ratio of our algorithm is 7+e for any e>;0. In the unsplittable flow problem on a path, we are given a capacitated path P and n tasks, each task having a demand, a profit, and start and end vertices. The goal is to compute a maximum profit set of tasks, such that for each edge e of P, the total demand of selected tasks that use e does not exceed the capacity of e. This is a well-studied problem that occurs naturally in various settings, and therefore it has been studied under alternative names, such as resource allocation, bandwidth allocation, resource constrained scheduling, temporal knapsack and interval packing. Polynomial time constant factor approximation algorithms for the problem were previously known only under the no-bottleneck assumption (in which the maximum task demand must be no greater than the minimum edge capacity). We introduce several novel algorithmic techniques, which might be of independent interest: a framework which reduces the problem to instances with a bounded range of capacities, and a new geometrically inspired dynamic program which solves a special case of the maximum weight independent set of rectangles problem to optimality. In addition, we show that the problem is strongly NP-hard even if all edge capacities are equal and all demands are either 1, 2, or 3.
ISBN:145771843X
9781457718434
ISSN:0272-5428
DOI:10.1109/FOCS.2011.10