As enterprises store more data, cloud computing has emerged as a powerful and popular paradigm on processing and analyzing the large-scale data. The cloud consumers can access the computing resources through cloud technologies and build their own computing platforms on virtual machines (VMs). The VMs will be placed on the hardware computing resources provided by the Cloud. An important problem is to allocate the VMs to the physical computers in an efficient way. For this issue, MapReduce has emerged as the leading platform to scale-out to large clusters of machines capable of processing PBytes of data. One of the biggest challenges from the perspective of the cloud provider is to offer this MapReduce service in the cloud effectively. Most cloud providers are focusing their attention on the runtime efficiency of the computers in the Cloud. The majority of studies converted the problem of mapping VMs to physical computers to be a Bin-packing problem, which is NP-Complete. In this paper, we propose algorithms for solving the problem of allocating VMs to physical computers with minimum run time. The problem is formulated as a 0/1 integer linear programming (0/1 ILP). Then, a rounding algorithm is proposed for obtaining a feasible solution.