Determine the best constants in planar connectivity algorithm exponents

Determine the best constants multiplying the square-root term in the exponents of exact algorithms for planar connectivity problems, whose running times are of the form \(2^{O(\sqrt n)}\).

Background

The paper explains that exact algorithms for several planar connectivity problems already achieve subexponential running times of the form 2O(n)2^{O(\sqrt n)}, and that this dependence is conditionally optimal under the SETH conjecture. Consequently, the principal unresolved issue identified at this point is not whether subexponential algorithms exist, but how small the leading constants in their exponents can be made.

References

The main open questions thus lie in determining the best constants for the $\Oh(\sqrt n)$ factor in the exponent.

— Faster Planar Graph Algorithms for Connectivity Problems via Meanders  (2610.11944 - Caroppo et al., 8 Oct 2026) in Section 1, Introduction and Overview, paragraph “Current Bounds”