Why does SQLite not use an index for queries on my many-to-many relation table? - performance

Question

It's been a while since I've written code, and I never used SQLite before, but many-to-many relationships used to be so fundamental, there must be a way to make them fast...
This is a abstracted version of my database:
CREATE TABLE a (_id INTEGER PRIMARY KEY, a1 TEXT NOT NULL);
CREATE TABLE b (_id INTEGER PRIMARY KEY, fk INTEGER NOT NULL REFERENCES a(_id));
CREATE TABLE d (_id INTEGER PRIMARY KEY, d1 TEXT NOT NULL);
CREATE TABLE c (_id INTEGER PRIMARY KEY, fk INTEGER NOT NULL REFERENCES d(_id));
CREATE TABLE b2c (fk_b NOT NULL REFERENCES b(_id), fk_c NOT NULL REFERENCES c(_id), CONSTRAINT PK_b2c_desc PRIMARY KEY (fk_b, fk_c DESC), CONSTRAINT PK_b2c_asc UNIQUE (fk_b, fk_c ASC));
CREATE INDEX a_a1 on a(a1);
CREATE INDEX a_id_and_a1 on a(_id, a1);
CREATE INDEX b_fk on b(fk);
CREATE INDEX b_id_and_fk on b(_id, fk);
CREATE INDEX c_id_and_fk on c(_id, fk);
CREATE INDEX c_fk on c(fk);
CREATE INDEX d_id_and_d1 on d(_id, d1);
CREATE INDEX d_d1 on d(d1);
I have put in any index i could think of, just to make sure (and more than is reasonable, but not a problem, since the data is read only). And yet on this query
SELECT count(*)
FROM a, b, b2c, c, d
WHERE a.a1 = "A"
AND a._id = b.fk
AND b._id = b2c.fk_b
AND c._id = b2c.fk_c
AND d._id = c.fk
AND d.d1 ="D";
the relation table b2c does not use any indexes:
0|0|2|SCAN TABLE b2c
0|1|1|SEARCH TABLE b USING INTEGER PRIMARY KEY (rowid=?)
0|2|0|SEARCH TABLE a USING INTEGER PRIMARY KEY (rowid=?)
0|3|3|SEARCH TABLE c USING INTEGER PRIMARY KEY (rowid=?)
0|4|4|SEARCH TABLE d USING INTEGER PRIMARY KEY (rowid=?)
The query is about two orders of magnitude to slow to be usable. Is there any way to make SQLite use an index on b2c?
Thanks!

Answer 1

In a nested loop join, the outermost table does not use an index for the join (because the database just goes through all rows anyway).
To be able to use an index for a join, the index and the other column must have the same affinity, which usually means that both columns must have the same type.
Change the types of the b2c columns to INTEGER.
If the lookups on a1 or d1 are very selective, using a or d as the outermost table might make sense, and would then allow to use an index for the filter.
Try running ANALYZE.
If that does not help, you can force the join order with CROSS JOIN or INDEXED BY.