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In computational complexity theory, a decision problem is NP-complete when it is both in NP and NP-hard. Although a solution to a NP-complete can be verified quickly, there is no known algorithm to solve it in polynomial time. There exists a method to reduce a SAT (Satifiability) problem to Subset Sum Problem (SSP) in the literature, however, it can only be applied to small or medium size problems. Our study is to find an efficient method to transform a SAT problem to a mixed integer linear programming problem in larger size. Observing the feature of variable-clauses constraints in SAT, we apply linear inequality model (LIM) to the problem and propose a method called LIMSAT. The new method can work efficiently for very large size problem with thousands of variables and clauses in SAT tested using up-to-date benchmarks.

In this paper, we apply an equivalent color transform (ECT) for a minimal $k$-coloring of any graph $G$. It contracts each color class of the graph to a single vertex and produces a complete graph $K_k$ for $G$ by removing redundant edges between any two vertices. Based on ECT, a simple proof for four color theorem for planar graph is then proposed., Comment: 4 pages, 1 figure

MapReduce is a popular parallel computing paradigm for Big Data processing in clusters and data centers. It is observed that different job execution orders and MapReduce slot configurations for a MapReduce workload have significantly different performance with regarding to the makespan, total completion time, system utilization and other performance metrics. There are quite a few algorithms on minimizing makespan of multiple MapReduce jobs. However, these algorithms are heuristic or suboptimal. The best known algorithm for minimizing the makespan is 3-approximation by applying Johnson rule. In this paper, we propose an approach called UAAS algorithm to meet the conditions of classical Johnson model. Then we can still use Johnson model for an optimal solution. We explain how to adapt to Johnson model and provide a few key features of our proposed method., Comment: Under Review of IEEE Trans. on Service Computing

In virtualized data centers, consolidation of Virtual Machines (VMs) on minimizing the number of total physical machines (PMs) has been recognized as a very efficient approach. This paper considers the energy-efficient consolidation of VMs in a Cloud Data center. Concentrating on CPU-intensive applications, the objective is to schedule all requests non-preemptively, subjecting to constraints of PM capacities and running time interval spans, such that the total energy consumption of all PMs is minimized (called MinTE for abbreviation). The MinTE problem is NP-complete in general. We propose a self-adaptive approached called SAVE. The approach makes decisions of the assignment and migration of VMs by probabilistic processes and is based exclusively on local information, therefore it is very simple to implement. Both simulation and real environment test show that our proposed method SAVE can reduce energy consumption about 30% against VMWare DRS and 10-20% against EcoCloud on average., Comment: Under Review of GlobalCom

The emergence of cloud computing based on virtualization technologies brings huge opportunities to host virtual resource at low cost without the need of owning any infrastructure. Virtualization technologies enable users to acquire, configure and be charged on pay-per-use basis. However, Cloud data centers mostly comprise heterogeneous commodity servers hosting multiple virtual machines (VMs) with potential various specifications and fluctuating resource usages, which may cause imbalanced resource utilization within servers that may lead to performance degradation and service level agreements (SLAs) violations. To achieve efficient scheduling, these challenges should be addressed and solved by using load balancing strategies, which have been proved to be NP-hard problem. From multiple perspectives, this work identifies the challenges and analyzes existing algorithms for allocating VMs to PMs in infrastructure Clouds, especially focuses on load balancing. A detailed classification targeting load balancing algorithms for VM placement in cloud data centers is investigated and the surveyed algorithms are classified according to the classification. The goal of this paper is to provide a comprehensive and comparative understanding of existing literature and aid researchers by providing an insight for potential future enhancements., Comment: 22 Pages, 4 Figures, 4 Tables, in press