Before revision:  In the absence of answer ordering, such a construction has been devised for the task of enumerating query answers of free-connex acyclic CQs, so that the access time is logarithmic. Moreover, it follows from past results that within the class of CQs without self-joins, being free-connex acyclic is necessary for the existence of such a construction (under conventional assumptions in fine-grained complexity). In this work, we embark on the challenge of identifying the  answer orderings that allow for ranked direct access with the above complexity guarantees.
After revision:  Specifically, we embark on the challenge of identifying the answer orderings that allow for ranked direct access with the above complexity guarantees.