Subquadratic algorithms for EWPM with real-valued coordinates

Determine whether there exists a subquadratic-time algorithm for computing the Euclidean minimum-weight perfect matching for two point sets in the plane when point coordinates are real-valued.

Background

For integer-grid inputs, faster algorithms are known (e.g., subquadratic in certain bounded-integer settings), but when coordinates are real numbers the best known general algorithms are quadratic-time.

The authors note that, unlike the non-bipartite Euclidean matching case where a subquadratic algorithm is known, the bipartite case with real coordinates lacks a proven subquadratic algorithm.