Fair Resource Allocation for Heterogeneous Tasks

We consider the problem of fair resource allocation for tasks where a resource can be assigned to at most one task, without any fractional allocation. The system is heterogeneous: capacity and cost may vary across resources, and different tasks may have different resource demand. Due to heterogeneity of resources, the cost of allocating a task in isolation, without any other competing task, may differ significantly from its allocation cost when the task is allocated along with other tasks. In this context, we consider the problem of allocating resource to tasks, while ensuring that the cost is distributed fairly across the tasks, namely, the ratio of allocation cost of a task to its isolation cost is minimized over all tasks. We show that this fair resource allocation problem is strongly NP-Hard even when the resources are of unit size by a reduction from 3-partition. Our central results are an LP rounding based algorithm with an approximation ratio of 2+ O(ϵ) for the problem when resources are of unit size, and a near-optimal greedy algorithm for a more restricted version. The above fair allocation problem arises for resource allocation in various context, such as, allocating computing resources for reservations requests from tenants in a data centre, allocating resources to computing tasks in grid computing, or allocating personnel for tasks in service delivery organizations.