“…Building on that work, Amanatidis, Markakis, Nikzad and Saberi [1] proved that for every constant ǫ, 0 < ǫ < 2/3, there is a polynomial-time algorithm finding an allocation guaranteeing to each agent at least (2/3 −ǫ) of A PRELIMINARY VERSION OF THE PAPER APPEARED IN THE PROCEEDINGS OF IJCAI 2018. 1 their maximin share (with the number of agents a part of the input). Ghodsi, Hajiaghayi, Seddighin, Seddighin and Yami [8] proved that in the results by Procaccia and Wang and by Amanatidis et al, the constant 2/3 can be replaced with 3/4.…”