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Tian W.,University of Science and Technology of China | Tian W.,City University of Hong Kong | Tian W.,USTC CityU Joint Research Institute | Li M.,City University of Hong Kong | Chen E.,University of Science and Technology of China
Theoretical Computer Science | Year: 2010

In this paper, we study the scheduling problem of jobs with multiple active intervals. Each job in the problem instance has n (n ≥ 1) disjoint active time intervals where it can be executed and a workload characterized by the required number of CPU cycles. Previously, people studied multiple interval job scheduling problem where each job must be assigned enough CPU cycles in one of its active intervals. We study a different practical version where the partial work done by the end of an interval remains valid and each job is considered finished if total CPU cycles assigned to it in all its active intervals reach the requirement. The goal is to find a feasible schedule that minimizes energy consumption. By adapting the algorithm for single interval jobs proposed in Yao, Demers and Shenker (1995) [1], one can still obtain an optimal schedule. However, the two phases in that algorithm (critical interval finding and scheduling the critical interval) can no longer be carried out directly. We present polynomial time algorithms to solve the two phases for jobs with multiple active intervals and therefore can still compute the optimal schedule in polynomial time. © 2009 Elsevier B.V. All rights reserved. Source


Tian W.,University of Science and Technology of China | Tian W.,City University of Hong Kong | Tian W.,USTC CityU Joint Research Institute | Xue C.J.,City University of Hong Kong | And 2 more authors.
Proceedings of the ACM Symposium on Applied Computing | Year: 2011

Stream processors are gaining popularity and getting deployed in many multimedia and scientific applications. Stream Register File (SRF) is a non-bypassing software-managed on-chip memory. It is a critical resource in stream processors. When loading a program from the off-chip memory into SRF for executing, the storage consumption and the data transfer time are two key factors which affect the performance. This work applies loop transformation to programs for SRF optimization. We consider two objectives of minimizing the storage consumption and data transfer time. Previous techniques concentrate on the utilization of SRF only. This is the first paper considering both the two factors. We present a cost evaluation function in this paper and apply loop fusion and reordering to improve the performance of stream processors. The experimental results show significant performance improvement. © 2011 ACM. Source


Chan Y.-K.,City University of Hong Kong | Li M.,City University of Hong Kong | Wu W.,City University of Hong Kong | Wu W.,Hefei University of Technology | Wu W.,USTC CityU Joint Research Institute
Journal of Combinatorial Optimization | Year: 2011

We study the probabilistic model in the key tree management problem. Users have different behaviors. Normal users have probability p to issue join/leave request while the loyal users have probability zero. Given the numbers of such users, our objective is to construct a key tree with minimum expected updating cost. We observe that a single LUN (Loyal User Node) is enough to represent all loyal users. When 1-p≤0.57 we prove that the optimal tree that minimizes the cost is a star. When 1-p>0.57, we try to bound the size of the subtree rooted at every non-root node. Based on the size bound, we construct the optimal tree using dynamic programming algorithm in O(n·K+K 4) time where K=min∈{4(log∈(1-p) -1) -1,n} and n is the number of normal users. © 2010 Springer Science+Business Media, LLC. Source


Wu W.,University of Science and Technology of China | Wu W.,City University of Hong Kong | Wu W.,USTC CityU Joint Research Institute | Li M.,City University of Hong Kong | Chen E.,University of Science and Technology of China
Theoretical Computer Science | Year: 2011

A dynamic voltage scaling technique provides the capability for processors to adjust the speed and control the energy consumption. We study the pessimistic accelerate model where the acceleration rate of the processor speed is at most K and jobs cannot be executed during the speed transition period. The objective is to find a min-energy (optimal) schedule that finishes every job within its deadline. The job set we study in this paper is aligned jobs where earlier released jobs have earlier deadlines. We start by investigating a special case where all jobs have a common arrival time and design an O(n2) algorithm to compute the optimal schedule based on some nice properties of the optimal schedule. Then, we study the general aligned jobs and obtain an O(n 2) algorithm to compute the optimal schedule by using the algorithm for the common arrival time case as a building block. Because our algorithm relies on the computation of the optimal schedule in the ideal model (K=∞), in order to achieve O(n2) complexity, we improve the complexity of computing the optimal schedule in the ideal model for aligned jobs from the currently best known O(n2logn) to O(n2). © 2010 Elsevier B.V. All rights reserved. Source


Tian W.,Hefei University of Technology | Tian W.,City University of Hong Kong | Tian W.,USTC CityU Joint Research Institute | Zhao Y.,City University of Hong Kong | And 10 more authors.
IEEE Transactions on Very Large Scale Integration (VLSI) Systems | Year: 2013

In this paper, we consider the task allocation problem on a hybrid main memory composed of nonvolatile memory (NVM) and dynamic random access memory (DRAM). Compared to the conventional memory technology DRAM, the emerging NVM has excellent energy performance since it consumes orders of magnitude less leakage power. On the other hand, most types of NVMs come with the disadvantages of much shorter write endurance and longer write latency as opposed to DRAM. By leveraging the energy efficiency of NVM and long write endurance of DRAM, this paper explores task allocation techniques on hybrid memory for multiple objectives such as minimizing the energy consumption, extending the lifetime, and minimizing the memory size. The contributions of this paper are twofold. First, we design the integer linear programming (ILP) formulations that can solve different objectives optimally. Then, we propose two sets of heuristic algorithms including three polynomial time offline heuristics and three online heuristics. Experiments show that compared to the optimal solutions generated by the ILP formulations, the offline heuristics can produce near-optimal results. © 1993-2012 IEEE. Source

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