  We consider allocating indivisible chores among agents with different cost
functions, such that all agents receive a cost of at most a constant factor
times their maximin share. The state-of-the-art was presented in In EC 2021 by
Huang and Lu. They presented a non-polynomial-time algorithm, called HFFD, that
attains an 11/9 approximation, and a polynomial-time algorithm that attains a
5/4 approximation.
  In this paper, we show that HFFD can be reduced to an algorithm called
MultiFit, developed by Coffman, Garey and Johnson in 1978 for makespan
minimization in job scheduling. Using this reduction, we prove that the
approximation ratio of HFFD is in fact equal to that of MultiFit, which is
known to be 13/11 in general, 20/17 for n at most 7, and 15/13 for n=3.
  Moreover, we develop an algorithm for (13/11+epsilon)-maximin-share
allocation for any epsilon>0, with run-time polynomial in the problem size and
1/epsilon. For n=3, we can improve the algorithm to find a 15/13-maximin-share
allocation with run-time polynomial in the problem size. Thus, we have
practical algorithms that attain the best known approximation to maximin-share
chore allocation.
