Randomized rounding: a technique for provably good algorithms and algorithmic proofs
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Proof verification and the hardness of approximation problems
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A constant factor approximation for the single sink edge installation problems
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A Survey of Energy Efficient Network Protocols for Wireless Networks
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A scheduling model for reduced CPU energy
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Online strategies for dynamic power management in systems with multiple power-saving states
ACM Transactions on Embedded Computing Systems (TECS)
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Convex Optimization
Hardness of Buy-at-Bulk Network Design
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On non-uniform multicommodity buy-at-bulk network design
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Algorithmic problems in power management
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Probability and Computing: Randomized Algorithms and Probabilistic Analysis
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Approximation Algorithms for Non-Uniform Buy-at-Bulk Network Design
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Speed scaling to manage energy and temperature
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The PCP theorem by gap amplification
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Energy efficient online deadline scheduling
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Reducing the Energy Consumption of Ethernet with Adaptive Link Rate (ALR)
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Reducing network energy consumption via sleeping and rate-adaptation
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Min-energy voltage allocation for tree-structured tasks
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Time-Slot Energy-Efficient Scheduling Algorithm for Capacity Limited Networks
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Identifying and using energy-critical paths
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Power efficient PoP design and auto-configuration
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Ant colony based self-adaptive energy saving routing for energy efficient Internet
Computer Networks: The International Journal of Computer and Telecommunications Networking
Energy-Efficient network routing with discrete cost functions
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Multicast routing for energy minimization using speed scaling
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We study network optimization that considers energy minimization as an objective. Studies have shown that mechanisms such as speed scaling can significantly reduce the power consumption of telecommunication networks by matching the consumption of each network element to the amount of processing required for its carried traffic. Most existing research on speed scaling focuses on a single network element in isolation. We aim for a network-wide optimization. Specifically, we study a routing problem with the objective of provisioning guaranteed speed/bandwidth for a given demand matrix while minimizing energy consumption. Optimizing the routes critically relies on the characteristic of the energy curve f(s), which is how energy is consumed as a function of the processing speed s. If f is superadditive, we show that there is no bounded approximation in general for integral routing, i.e., each traffic demand follows a single path. This contrasts with the well-known logarithmic approximation for subadditive functions. However, for common energy curves such as polynomials f(s) = µsα, we are able to show a constant approximation via a simple scheme of randomized rounding. The scenario is quite different when a non-zero startup cost σ appears in the energy curve, e.g. f(s) = {0 σ + µsα if s =0 if s 0. For this case a constant approximation is no longer feasible. In fact, for any α 1, we show an Ω(log1/4 N hardness result under a common complexity assumption. (Here N is the size of the network.) On the positive side we present O((σ/µ)1/α) and O(K) approximations, where K is the number of demands.