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- All Subjects: Approximation Algorithms
- Creators: Konjevod, Goran
- Creators: Richa, Andréa W.
Description
Semiconductor scaling technology has led to a sharp growth in transistor counts. This has resulted in an exponential increase on both power dissipation and heat flux (or power density) in modern microprocessors. These microprocessors are integrated as the major components in many modern embedded devices, which offer richer features and attain higher performance than ever before. Therefore, power and thermal management have become the significant design considerations for modern embedded devices. Dynamic voltage/frequency scaling (DVFS) and dynamic power management (DPM) are two well-known hardware capabilities offered by modern embedded processors. However, the power or thermal aware performance optimization is not fully explored for the mainstream embedded processors with discrete DVFS and DPM capabilities. Many key problems have not been answered yet. What is the maximum performance that an embedded processor can achieve under power or thermal constraint for a periodic application? Does there exist an efficient algorithm for the power or thermal management problems with guaranteed quality bound? These questions are hard to be answered because the discrete settings of DVFS and DPM enhance the complexity of many power and thermal management problems, which are generally NP-hard. The dissertation presents a comprehensive study on these NP-hard power and thermal management problems for embedded processors with discrete DVFS and DPM capabilities. In the domain of power management, the dissertation addresses the power minimization problem for real-time schedules, the energy-constrained make-span minimization problem on homogeneous and heterogeneous chip multiprocessors (CMP) architectures, and the battery aware energy management problem with nonlinear battery discharging model. In the domain of thermal management, the work addresses several thermal-constrained performance maximization problems for periodic embedded applications. All the addressed problems are proved to be NP-hard or strongly NP-hard in the study. Then the work focuses on the design of the off-line optimal or polynomial time approximation algorithms as solutions in the problem design space. Several addressed NP-hard problems are tackled by dynamic programming with optimal solutions and pseudo-polynomial run time complexity. Because the optimal algorithms are not efficient in worst case, the fully polynomial time approximation algorithms are provided as more efficient solutions. Some efficient heuristic algorithms are also presented as solutions to several addressed problems. The comprehensive study answers the key questions in order to fully explore the power and thermal management potentials on embedded processors with discrete DVFS and DPM capabilities. The provided solutions enable the theoretical analysis of the maximum performance for periodic embedded applications under power or thermal constraints.
ContributorsZhang, Sushu (Author) / Chatha, Karam S (Thesis advisor) / Cao, Yu (Committee member) / Konjevod, Goran (Committee member) / Vrudhula, Sarma (Committee member) / Xue, Guoliang (Committee member) / Arizona State University (Publisher)
Created2012
Description
This thesis addresses the following fundamental maximum throughput routing problem: Given an arbitrary edge-capacitated n-node directed network and a set of k commodities, with source-destination pairs (s_i,t_i) and demands d_i> 0, admit and route the largest possible number of commodities -- i.e., the maximum throughput -- to satisfy their demands.
The main contributions of this thesis are three-fold: First, a bi-criteria approximation algorithm is presented for this all-or-nothing multicommodity flow (ANF) problem. This algorithm is the first to achieve a constant approximation of the maximum throughput with an edge capacity violation ratio that is at most logarithmic in n, with high probability. The approach used is based on a version of randomized rounding that keeps splittable flows, rather than approximating those via a non-splittable path for each commodity: This allows it to work for arbitrary directed edge-capacitated graphs, unlike most of the prior work on the ANF problem. The algorithm also works if a weighted throughput is considered, where the benefit gained by fully satisfying the demand for commodity i is determined by a given weight w_i>0. Second, a derandomization of the algorithm is presented that maintains the same approximation bounds, using novel pessimistic estimators for Bernstein's inequality. In addition, it is shown how the framework can be adapted to achieve a polylogarithmic fraction of the maximum throughput while maintaining a constant edge capacity violation, if the network capacity is large enough. Lastly, one important aspect of the randomized and derandomized algorithms is their simplicity, which lends to efficient implementations in practice. The implementations of both randomized rounding and derandomized algorithms for the ANF problem are presented and show their efficiency in practice.
The main contributions of this thesis are three-fold: First, a bi-criteria approximation algorithm is presented for this all-or-nothing multicommodity flow (ANF) problem. This algorithm is the first to achieve a constant approximation of the maximum throughput with an edge capacity violation ratio that is at most logarithmic in n, with high probability. The approach used is based on a version of randomized rounding that keeps splittable flows, rather than approximating those via a non-splittable path for each commodity: This allows it to work for arbitrary directed edge-capacitated graphs, unlike most of the prior work on the ANF problem. The algorithm also works if a weighted throughput is considered, where the benefit gained by fully satisfying the demand for commodity i is determined by a given weight w_i>0. Second, a derandomization of the algorithm is presented that maintains the same approximation bounds, using novel pessimistic estimators for Bernstein's inequality. In addition, it is shown how the framework can be adapted to achieve a polylogarithmic fraction of the maximum throughput while maintaining a constant edge capacity violation, if the network capacity is large enough. Lastly, one important aspect of the randomized and derandomized algorithms is their simplicity, which lends to efficient implementations in practice. The implementations of both randomized rounding and derandomized algorithms for the ANF problem are presented and show their efficiency in practice.
ContributorsChaturvedi, Anya (Author) / Richa, Andréa W. (Thesis advisor) / Sen, Arunabha (Committee member) / Schmid, Stefan (Committee member) / Arizona State University (Publisher)
Created2020