Express Nearest Neighbor Join in Postgresql? - postgresql

Question

I have two tables Q and T, both containing a column of float numbers.
What I want to do is, for each number in Q, I want to find a number in T that has the smallest distance to it.
For example, for T={1,7,9} and Q={2,6,10}, I want to return Q,T pairs as {(2,1),(6,7),(10,9)}.
How should I express this query with SQL?
In addition, is that possible to accelerate this join by index, e.g. add an operator class which bind "FOR ORDER BY <->" with fabs calculation?

Answer 1

create table t (val_t integer);
create table q (val_q integer);
insert into t values (1),(7),(9);
insert into q values (2),(6),(10);
Start with a query that cross joins the two tables and adds a rank based on the difference:
SELECT val_q, val_t, rank() OVER (PARTITION BY val_q ORDER BY abs(val_t - val_q))
FROM t
JOIN q ON true ;
Use this query in a cte or subquery and filter by rank:
WITH src AS(
SELECT val_q, val_t, rank() OVER (PARTITION BY val_q ORDER BY abs(val_t - val_q))
FROM t
JOIN q ON true )
SELECT val_q, val_t FROM src
WHERE rank = 1;
val_q | val_t
-------+-------
2 | 1
6 | 7
10 | 9
See https://www.postgresql.org/docs/12/tutorial-window.html

Answer 2

Given this schema:
create table t (tn float);
insert into t values (1), (7), (9);
create table q (qn float);
insert into q values (2), (6), (10);
DISTINCT ON is the most straightforward way:
select distinct on (qn) qn, tn
from q
cross join t
order by qn, abs(qn - tn);
Exploiting a numeric range may perform better depending on your data sizes. If performance is an issue, then you can create an actual temp table for the range_tn CTE and put a gist index on it:
with all_tn as (
select tn
from t
union select null
), range_tn as (
select numrange(tn::numeric, (lead(tn) over w)::numeric, '[]') as tr
from all_tn
window w as (order by tn nulls first)
)
select qn,
case
when lower_inf(tr) then upper(tr)
when upper_inf(tr) then lower(tr)
when 2 * qn - lower(tr) - upper(tr) > 0 then upper(tr)
else lower(tr)
end as tn
from q
join range_tn
on qn::numeric <# tr;
Fiddle here