The proposed algorithms can be extended to handle infinite metric spaces, such as the full Euclidean space, by leveraging the properties of uniform coincidence constraints that are closed under addition. The key insight is that if the coincidence constraint allows for the addition of profiles, we can utilize a 2-approximation strategy. This involves constructing a repair by moving each cell to the nearest valid point in the infinite metric space, ensuring that the total movement does not exceed twice the optimal cost.
To implement this efficiently, we can utilize sampling techniques to identify potential points in the infinite space that are close to the existing values in the database. By focusing on a finite subset of points that are representative of the infinite space, we can apply the existing algorithms designed for finite metrics. Additionally, the use of probabilistic tree embeddings can facilitate the approximation of distances in the infinite metric space, allowing for a more efficient computation of repairs while maintaining the integrity constraints.