Lowering the exponent for CSPs with k-edge terms

Determine whether the exponent in the known polynomial-time algorithm for constraint satisfaction problems induced by a k-edge term can be reduced to O(k), extending the quadratic-time result established for Maltsev constraints, which correspond to the case k = 2.

Background

The paper develops an O(d5 n2 I)-time algorithm for Maltsev constraint satisfaction problems, improving the previously known O(n4 m) bound for fixed finite languages. Maltsev operations are the k = 2 special case of k-edge terms.

The authors note that several components of their algorithm extend to k-edge terms. The currently known algorithm for the corresponding CSPs has exponent (k+2)2 in its running-time bound, and the paper identifies as unresolved whether this exponent can be reduced all the way to O(k).

References

However, whether the exponent can actually reach $O(k)$ is an intriguing open question.

— A Fast Algorithm for Maltsev Constraints  (2610.08207 - Lagerkvist, 6 Oct 2026) in Section 1, paragraph beginning “This work naturally opens up corresponding questions”