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 \nc{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 \NPH 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.

翻译：将冲突性工作分配给个体，同时为每个个体考虑预算约束，是出现在多种现实场景中的优化问题。本文考虑每个个体从每项工作中获得一定满意度的情况。我们致力于找到一种可行的冲突性工作分配方案，以最大化公平成本，即最差处境个体的满意度。据我们所知，这是首次将公平性、预算可行性和冲突避免相结合的研究。我们系统研究了寻找预算可行且无冲突的公平分配的计算复杂性，并表明该问题推广了大量经典优化问题。因此，不足为奇的是，即使在只有两个个体且工作间无冲突的情况下，该问题也是NP难的。我们证明，该问题在近似算法和参数化算法领域中存在算法，这些算法利用一系列自然参数，其运行时间与已知算法相当甚至更优。