The maximum concurrent flow problem
Journal of the ACM (JACM)
Fast approximation algorithms for fractional packing and covering problems
Mathematics of Operations Research
Fast deterministic approximation for the multicommodity flow problem
Mathematical Programming: Series A and B
Approximating Fractional Multicommodity Flow Independent of the Number of Commodities
SIAM Journal on Discrete Mathematics
Measuring ISP topologies with rocketfuel
Proceedings of the 2002 conference on Applications, technologies, architectures, and protocols for computer communications
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
Development and implementation of heuristic algorithms for multicommodity flow problems
Development and implementation of heuristic algorithms for multicommodity flow problems
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Improved Combinatorial Algorithms for Facility Location Problems
SIAM Journal on Computing
Approximating Fractional Packings and Coverings in O(1/epsilon) Iterations
SIAM Journal on Computing
The DLT priority sampling is essentially optimal
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Confidence intervals for priority sampling
SIGMETRICS '06/Performance '06 Proceedings of the joint international conference on Measurement and modeling of computer systems
Priority sampling for estimation of arbitrary subset sums
Journal of the ACM (JACM)
Faster and Simpler Algorithms for Multicommodity Flow and Other Fractional Packing Problems
SIAM Journal on Computing
Beating Simplex for Fractional Packing and Covering Linear Programs
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Proceedings of the forty-second ACM symposium on Theory of computing
Optimal content placement for a large-scale VoD system
Proceedings of the 6th International COnference
Heuristic improvements for computing maximum multicommodity flow and minimum multicut
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Solving LP relaxations of large-scale precedence constrained problems
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
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We empirically study the exponential potential function (EPF) approach to linear programming (LP), as applied to optimizing content placement in a video-on-demand (VoD) system. Even instances of modest size (e.g., 50 servers and 20k videos) stretch the capabilities of LP solvers such as CPLEX. These are packing LPs with block-diagonal structure, where the blocks are fractional uncapacitated facility location (UFL) problems. Our implementation of the EPF framework allows us to solve large instances to 1% accuracy 2000x faster than CPLEX, and scale to instances much larger than CPLEX can handle on our hardware. Starting from the packing LP code described by Bienstock [4], we add many innovations. Our most interesting one uses priority sampling to shortcut lower bound computations, leveraging fast block heuristics to magnify these benefits. Other impactful changes include smoothing the duals to obtain effective Lagrangian lower bounds, shuffling the blocks after every round-robin pass, and better ways of searching for OPT and adjusting a critical scale parameter. By documenting these innovations and their practical impact on our testbed of synthetic VoD instances designed to mimic the proprietary instances that motivated this work, we aim to give a head-start to researchers wishing to apply the EPF framework in other practical domains.