Resource allocation for covering time varying demands
ESA'11 Proceedings of the 19th European conference on Algorithms
Distributed algorithms for scheduling on line and tree networks
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Constant integrality gap LP formulations of unsplittable flow on a path
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
A constant factor approximation algorithm for the storage allocation problem: extended abstract
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
Scheduling jobs with multiple non-uniform tasks
Euro-Par'13 Proceedings of the 19th international conference on Parallel Processing
A logarithmic approximation for unsplittable flow on line graphs
ACM Transactions on Algorithms (TALG)
Approximation algorithms for the ring loading problem with penalty cost
Information Processing Letters
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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 e0. 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.