PPAD membership for contiguous EF1 outer chore divisions

Determine whether computing a contiguous EF1 outer division of indivisible chores on a path belongs to PPAD.

Background

The paper extends its reduction from additive cake valuations to additive chore costs and obtains PPAD-hardness for contiguous approximate envy-free chore divisions, as well as PPAD-completeness for the corresponding cake-division problems. It then applies a quantile transfer to obtain PPAD-hardness for contiguous EFc divisions of indivisible chores on a path. However, although the cited literature establishes the existence of contiguous EF1 outer chore divisions, the computational membership of this problem in PPAD is not resolved.