Polynomial Methods for Separable Convex Optimization in Unimodular Linear Spaces with Applications
SIAM Journal on Computing
Voltage scheduling problem for dynamically variable voltage processors
ISLPED '98 Proceedings of the 1998 international symposium on Low power electronics and design
Solving the Convex Cost Integer Dual Network Flow Problem
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
Dynamic Voltage Scaling with Links for Power Optimization of Interconnection Networks
HPCA '03 Proceedings of the 9th International Symposium on High-Performance Computer Architecture
Energy-Aware Partitioning for Multiprocessor Real-Time Systems
IPDPS '03 Proceedings of the 17th International Symposium on Parallel and Distributed Processing
Energy Aware Scheduling for Distributed Real-Time Systems
IPDPS '03 Proceedings of the 17th International Symposium on Parallel and Distributed Processing
Multiprocessor Energy-Efficient Scheduling for Real-Time Tasks with Different Power Characteristics
ICPP '05 Proceedings of the 2005 International Conference on Parallel Processing
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
Leakage-Aware Multiprocessor Scheduling
Journal of Signal Processing Systems
A variable frequency link for a power-aware network-on-chip (NoC)
Integration, the VLSI Journal
On the Performance of Greedy Algorithms for Power Consumption Minimization
ICPP '11 Proceedings of the 2011 International Conference on Parallel Processing
Speed scaling of tasks with precedence constraints
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Power-aware Manhattan Routing on Chip Multiprocessors
IPDPS '12 Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium
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In single chip multiprocessors (CMP) with grid topologies, a significant part of power consumption is attributed to communications between the cores of the grid. We investigate the problem of routing communications between CMP cores using shortest paths, in a model in which the power cost associated with activating a communication link at a transmission speed of f bytes/second is proportional to fα, for some constant exponent α2. Our main result is a trade-off showing how the power required for communication in CMP grids depends on the ability to split communication requests between a given pair of node, routing each such request along multiple paths. For a pair of cores in a m ×n grid, the number of available communication paths between them grows exponentially with n,m. By contrast, we show that optimal power consumption (up to constant factors) can be achieved by splitting each communication request into k paths, starting from a threshold value of $k = \Theta (n^{1/\left(\alpha-1\right)})$. This threshold is much smaller than n for typical values of α≈3, and may be considered practically feasible for use in routing schemes on the grid. More generally, we provide efficient algorithms for routing multiple k-splittable communication requests between two cores in the grid, providing solutions within a constant approximation of the optimum cost. We support our results with algorithm simulations, showing that for practical instances, our approach using k-splittable requests leads to a power cost close to that of the optimal solution with arbitrarily splittable requests, starting from the stated threshold value of k.