I have two tables at my disposal, one work dataset and one reference dataset. Each dataset has got two columns, lets say these are fields A and B. I would like the rows in reference dataset with the rows in work dataset that are 'closest' w.r.t. some distance. I have more rows in work dataset than in reference dataset, and i will match all rows in reference dataset to some rows in work dataset.

I can define distance between two rows in reference and wrk dataset like this:

$ d_{i,j} = (A_{w}(i) - A_{r}(j))^{2} + (B_{w}(i) - B_{r}(j))^{2} $

with $A_{w}, A_{r}, B_{w}, B_{r} $ the A and B columns work and reference datasets with obvious notation.

In other word, i want to minimize over all permutations of rows from the work dataset (with the same number of rows as in reference dataset) the sum of distances between one row in reference dataset and one row in wrk dataset.

I do not know how to proceed if not examining all permutations.

This is combinatorial problem. What about stochastic methods: genetic algorithm, swarm...

Could you hint at some idea for a start ?

I had a look at linear assignment problem. However, my problem is not a complete bipartatite graph representation, it is not complete since there can be more peaks in work signal than there are in reference signal.

Thanks !