  We initiate the study of indivisible chore allocation for agents with
asymmetric shares. The fairness concept we focus on is the weighted natural
generalization of maxmin share: WMMS fairness and OWMMS fairness. We first
highlight the fact that commonly used algorithms that work well for the
allocation of goods to asymmetric agents, and even for chores to symmetric
agents do not provide good approximations for allocation of chores to
asymmetric agents under WMMS. As a consequence, we present a novel
polynomial-time constant-approximation algorithm, via linear program, for
OWMMS. For two special cases: the binary valuation case and the 2-agent case,
we provide exact or better constant-approximation algorithms.
