Budget-feasible Egalitarian Allocation of Conflicting Jobs
CoRR(2024)
摘要
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 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.
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