  Multi-robot task allocation is one of the most fundamental classes of
problems in robotics and is crucial for various real-world robotic applications
such as search, rescue and area exploration. We consider the Single-Task robots
and Multi-Robot tasks Instantaneous Assignment (ST-MR-IA) setting where each
task requires at least a certain number of robots and each robot can work on at
most one task and incurs an operational cost for each task. Our aim is to
consider a natural computational problem of allocating robots to complete the
maximum number of tasks subject to budget constraints. We consider budget
constraints of three different kinds: (1) total budget, (2) task budget, and
(3) robot budget. We provide a detailed complexity analysis including results
on approximations as well as polynomial-time algorithms for the general setting
and important restricted settings.
