TITLE: How hard is it to compute the Davenport constant?
QUESTION [8 upvotes]: The Davenport constant $D(G)$ of a finite abelian group $(G,+)$ is the least positive integer $k$ such that every sequence in $G$ of length $k$ has a zero-sum (nonempty) subsequence.
It seems that the Davenport constant is explicitly known only in a handful of cases (such as when $G$ is cyclic, or is a $p$-group, or has rank $2$). Is anything known about how hard it is to compute the Davenport constant?

REPLY [8 votes]: The Davenport constants for all groups of order less than thirty-two is computed in arXiv.1702.02997, using GAP. The algorithm is presented and the complexity is discussed in section 6. The run-time varies by orders of magnitude from one group to another, dependent on the number of equivalence classes that need to be considered.