Efficient Algorithms for Envy-Free Stick Division With Fewest Cuts

Segal-Halevi, Hassidim, and Aumann (AAMAS, 2015) propose the problem of cutting sticks so that at least k sticks have equal length and no other stick is longer. This allows for an envy-free allocation of sticks to k players, one each. The resulting number of sticks should also be minimal. We analyze the structure of this problem and devise a linear-time algorithm for it.