minimizing the rent cost with deadline constraints [@BOT1; @BOT2; @BOT3; @HCOC1; @HCOC2; @UCC13; @reusable] or minimizing the makespan [@FermiCloud; @CBS1; @CBS2] for scientific computing applications by deciding which tasks should be outsourced to the public cloud. While, these works do not consider how the local cloud/cluster provisions resources, i.e. they do not provide the mapping between physical machines (PM) and provisioned resources in the local cloud.

Only a few hybrid cloud managements [@Aneka1; @Aneka2; @Aneka3] have coordinated dynamic provisioning and scheduling that is able to cost-effectively complete applications within their respective deadlines. While these works separately scheduled tasks and provisioned resources, i.e., they first decided how many resources, each of which is either a VM in public cloud or a PM in local cloud(s)/cluster(s), used for running tasks and then provisioned the resources from the resource pool, considering that all of the resources are homogeneous.

Different from these existing works, we study on cost-efficiently mapping the tasks to the resources for deadline-constrained Bag-of-Tasks (BoT) jobs, a kind of very common application in the parallel and distributed systems [@common1; @common2], such as parallel image rendering, data analysis, and software testing [@BoTimage; @BoTdata; @BoTtest], on a hybrid cloud with heterogeneous local resources. 