Budget-feasible egalitarian allocation of conflicting jobs

Allocating conflicting jobs among individuals while respecting a budget constraint for each individual is an optimization problem that arises in various real-world scenarios. In this paper, we consider the situation where each individual derives some satisfaction from each job. We focus on finding a feasible allocation of conflicting jobs that maximize egalitarian cost, i.e., the satisfaction of the individual who is worst-off. To the best of our knowledge, this is the first paper to combine egalitarianism, budget-feasibility, and conflict-freeness in allocations. We provide a systematic study of the computational complexity of finding budget-feasible conflict-free egalitarian allocation and show that our problem generalizes a large number of classical optimization problems. Therefore, unsurprisingly, our problem is NP-hard even for two individuals and when there is no conflict between any jobs. We show that the problem admits algorithms when studied in the realm of approximation algorithms and parameterized algorithms with a host of natural parameters that match and in some cases improve upon the running time of known algorithms.