Task consolidation is a way of maximizing cloud computing resource, which brings many benefits such as better use of resources, rationalization of maintenance, IT service customization, QoS and reliable services, etc. However, maximizing resource utilization does not mean efficient energy usage. Many literature show that energy consumption and resource utilization in clouds are highly coupled. Some research works aim to decrease resource utilization for saving energy while some try to find the balance between resource utilization and energy consumption. In this paper, an energy-aware task consolidation (ETC) technique is presented aims to optimize energy consumption of virtual clusters in cloud data center. Conforming most cloud systems, a 70% principle of CPU utilization is proposed to manage task consolidation among virtual clusters. The simulation results show that ETC can significantly reduce power consumption in managing task consolidation for cloud systems. Up to 17% improvement as compare to a recent work in [10] that aims to maximize resource utilization can be obtained.

Functional dependency is concerned with rewriting a Boolean function f as a function h over a set of base functions {g1,¿,gn}, i.e., f = h(g1,¿,gn). It plays an important role in many aspects of electronic design automation (EDA). Prior approaches to the exploration of functional dependency are based on binary decision diagrams (BDDs), which may not be easily scalable to large designs. This paper formulates both single-output and multiple-output functional dependencies as satisfiability (SAT) solving and exploits extensively the capability of a modern SAT solver. Thereby, functional dependency can be detected effectively through incremental SAT solving, and the dependency function h, if it exists, is obtained through Craig interpolation. The proposed method enables (1) scalable detection of functional dependency, (2) fast enumeration of dependency function under a large set of candidate base functions, and (3) potential application to large-scale logic synthesis and formal verification. Experimental results show that the proposed method is far superior to prior work and scales well in dealing with the largest ISCAS and ITC benchmark circuits with up to 200 K gates.

Functional dependency is concerned with rewriting a Boolean function f as a function h over a set of base functions {g1, ..., gn), i.e. f = h(g1, ..., gn). It plays an important role in many aspects of electronic design automation (EDA), ranging from logic synthesis to formal verification. Prior approaches to the exploration of functional dependency are based on binary decision diagrams (BDDs), which may not be easily scalable to large designs. This paper proposes a novel reformulation that extensively exploits the capability of modern satisfiability (SAT) solvers. Thereby, functional dependency is detected effectively through incremental SAT solving, and the dependency function h, if it exists, is obtained through Craig interpolation. The main strengths of the proposed approach include: (1) fast detection of functional dependency with modest memory consumption and thus scalable to large designs, (2) a full capacity to handle a large set of base functions and thus discovering dependency whenever exists, and (3) potential application to large-scale logic optimization and verification reduction. Experimental results show the proposed method is far superior to prior work and scales well in dealing with the largest ISCAS89 and ITC99 benchmark circuits with up to 200 K gates.