Polyhedral characterization of discrete dynamic programming
Operations Research
On approximating rectangle tiling and packing
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
A unified approach to approximating resource allocation and scheduling
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Improved approximation algorithms for rectangle tiling and packing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Improved Approximation Algorithms for Resource Allocation
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
A quasi-PTAS for unsplittable flow on line graphs
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Multicommodity demand flow in a tree and packing integer programs
ACM Transactions on Algorithms (TALG)
A logarithmic approximation for unsplittable flow on line graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Maximum independent set of rectangles
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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
Resource allocation with time intervals
Theoretical Computer Science
Caching is hard: even in the fault model
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
A Constant Factor Approximation Algorithm for Unsplittable Flow on Paths
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
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The Unsplittable Flow Problem on a Path (UFPP) is a core problem in many important settings such as network flows, bandwidth allocation, resource constraint scheduling, and interval packing. We are given a path with capacities on the edges and a set of tasks, each task having a demand, a profit, a source and a destination vertex on the path. The goal is to compute a subset of tasks of maximum profit that does not violate the edge capacities. In practical applications generic approaches such as integer programming (IP) methods are desirable. Unfortunately, no IP-formulation is known for the problem whose LP-relaxation has an integrality gap that is provably constant. For the unweighted case, we show that adding a few constraints to the standard LP of the problem is sufficient to make the integrality gap drop from Ω(n) to O(1). This positively answers an open question in [Chekuri et al., APPROX 2009]. For the general (weighted) case, we present an extended formulation with integrality gap bounded by 7+ε. This matches the best known approximation factor for the problem [Bonsma et al., FOCS 2011]. This result exploits crucially a technique for embedding dynamic programs into linear programs. We believe that this method could be useful to strengthen LP-formulations for other problems as well and might eventually speed up computations due to stronger problem formulations.