Complexity class membership of Euclidean Minimum-Weight Perfect Matching (EWPM) in the bit-complexity model

Ascertain whether the Euclidean minimum-weight perfect matching problem on complete bipartite graphs in the bit-complexity model belongs to the class P or to NP.

Background

In the bit-complexity model, edge weights are Euclidean distances, which can be irrational, complicating comparisons and arithmetic.

The authors note that existing algorithms for EWPM typically rely on comparing sums of square roots, for which the computational complexity is not settled, and consequently the overall complexity status of EWPM in this model is unclear.