Fair Interval Scheduling of Indivisible Chores
CoRR(2024)
摘要
We study the problem of fairly assigning a set of discrete tasks (or chores)
among a set of agents with additive valuations. Each chore is associated with a
start and finish time, and each agent can perform at most one chore at any
given time. The goal is to find a fair and efficient schedule of the chores,
where fairness pertains to satisfying envy-freeness up to one chore (EF1) and
efficiency pertains to maximality (i.e., no unallocated chore can be feasibly
assigned to any agent). Our main result is a polynomial-time algorithm for
computing an EF1 and maximal schedule for two agents under monotone valuations
when the conflict constraints constitute an arbitrary interval graph. The
algorithm uses a coloring technique in interval graphs that may be of
independent interest. For an arbitrary number of agents, we provide an
algorithm for finding a fair schedule under identical dichotomous valuations
when the constraints constitute a path graph. We also show that stronger
fairness and efficiency properties, including envy-freeness up to any chore
(EFX) along with maximality and EF1 along with Pareto optimality, cannot be
achieved.
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