PostgreSQL: The lower the LIMIT, the slower the query

Question

I have the following query

SELECT translation.id
FROM "TRANSLATION" translation
   INNER JOIN "UNIT" unit
     ON translation.fk_id_unit = unit.id
   INNER JOIN "DOCUMENT" document
     ON unit.fk_id_document = document.id
WHERE document.fk_id_job = 3665
ORDER BY translation.id asc
LIMIT 50

It runs for dreadful 110 seconds.

The table sizes:

+----------------+-------------+
| Table          | Records     |
+----------------+-------------+
| TRANSLATION    |  6,906,679  |
| UNIT           |  6,906,679  |
| DOCUMENT       |     42,321  |
+----------------+-------------+

However, when I change the LIMIT parameter from 50 to 1000, the query finishes in 2 seconds.

Here is the query plan for the slow one

Limit (cost=0.00..146071.52 rows=50 width=8) (actual time=111916.180..111917.626 rows=50 loops=1)
  ->  Nested Loop (cost=0.00..50748166.14 rows=17371 width=8) (actual time=111916.179..111917.624 rows=50 loops=1)
      Join Filter: (unit.fk_id_document = document.id)
    ->  Nested Loop (cost=0.00..39720545.91 rows=5655119 width=16) (actual time=0.051..15292.943 rows=5624514 loops=1)
          ->  Index Scan using "TRANSLATION_pkey" on "TRANSLATION" translation (cost=0.00..7052806.78 rows=5655119 width=16) (actual time=0.039..1887.757 rows=5624514 loops=1)
          ->  Index Scan using "UNIT_pkey" on "UNIT" unit (cost=0.00..5.76 rows=1 width=16) (actual time=0.002..0.002 rows=1 loops=5624514)
              Index Cond: (unit.id = translation.fk_id_translation_unit)
    ->  Materialize  (cost=0.00..138.51 rows=130 width=8) (actual time=0.000..0.006 rows=119 loops=5624514)
          ->  Index Scan using "DOCUMENT_idx_job" on "DOCUMENT" document (cost=0.00..137.86 rows=130 width=8) (actual time=0.025..0.184 rows=119 loops=1)
              Index Cond: (fk_id_job = 3665)

and for the fast one

Limit (cost=523198.17..523200.67 rows=1000 width=8) (actual time=2274.830..2274.988 rows=1000 loops=1)
  ->  Sort (cost=523198.17..523241.60 rows=17371 width=8) (actual time=2274.829..2274.895 rows=1000 loops=1)
      Sort Key: translation.id
      Sort Method:  top-N heapsort  Memory: 95kB
      ->  Nested Loop (cost=139.48..522245.74 rows=17371 width=8) (actual time=0.095..2252.710 rows=97915 loops=1)
          ->  Hash Join (cost=139.48..420861.93 rows=17551 width=8) (actual time=0.079..2005.238 rows=97915 loops=1)
              Hash Cond: (unit.fk_id_document = document.id)
              ->  Seq Scan on "UNIT" unit  (cost=0.00..399120.41 rows=5713741 width=16) (actual time=0.008..1200.547 rows=6908070 loops=1)
              ->  Hash (cost=137.86..137.86 rows=130 width=8) (actual time=0.065..0.065 rows=119 loops=1)
                  Buckets: 1024  Batches: 1  Memory Usage: 5kB
                  ->  Index Scan using "DOCUMENT_idx_job" on "DOCUMENT" document (cost=0.00..137.86 rows=130 width=8) (actual time=0.009..0.041 rows=119 loops=1)
                      Index Cond: (fk_id_job = 3665)
          ->  Index Scan using "TRANSLATION_idx_unit" on "TRANSLATION" translation (cost=0.00..5.76 rows=1 width=16) (actual time=0.002..0.002 rows=1 loops=97915)
              Index Cond: (translation.fk_id_translation_unit = unit.id)

Apparently the execution plans are very different and the second one results in a query 50 times faster.

I have indexes on all the fields involved in the query and I ran ANALYZE on all tables just before running the queries.

Can somebody see what is wrong with the first query?

UPDATE: Table definitions

CREATE TABLE "public"."TRANSLATION" (
  "id" BIGINT NOT NULL, 
  "fk_id_translation_unit" BIGINT NOT NULL, 
  "translation" TEXT NOT NULL, 
  "fk_id_language" INTEGER NOT NULL, 
  "relevance" INTEGER, 
  CONSTRAINT "TRANSLATION_pkey" PRIMARY KEY("id"), 
  CONSTRAINT "TRANSLATION_fk" FOREIGN KEY ("fk_id_translation_unit")
    REFERENCES "public"."UNIT"("id")
    ON DELETE CASCADE
    ON UPDATE NO ACTION
    DEFERRABLE
    INITIALLY DEFERRED, 
  CONSTRAINT "TRANSLATION_fk1" FOREIGN KEY ("fk_id_language")
    REFERENCES "public"."LANGUAGE"("id")
    ON DELETE NO ACTION
    ON UPDATE NO ACTION
    NOT DEFERRABLE
) WITHOUT OIDS;

CREATE INDEX "TRANSLATION_idx_unit" ON "public"."TRANSLATION"
  USING btree ("fk_id_translation_unit");

CREATE INDEX "TRANSLATION_language_idx" ON "public"."TRANSLATION"
  USING hash ("translation");

---

CREATE TABLE "public"."UNIT" (
  "id" BIGINT NOT NULL, 
  "text" TEXT NOT NULL, 
  "fk_id_language" INTEGER NOT NULL, 
  "fk_id_document" BIGINT NOT NULL, 
  "word_count" INTEGER DEFAULT 0, 
  CONSTRAINT "UNIT_pkey" PRIMARY KEY("id"), 
  CONSTRAINT "UNIT_fk" FOREIGN KEY ("fk_id_document")
    REFERENCES "public"."DOCUMENT"("id")
    ON DELETE CASCADE
    ON UPDATE NO ACTION
    NOT DEFERRABLE, 
  CONSTRAINT "UNIT_fk1" FOREIGN KEY ("fk_id_language")
    REFERENCES "public"."LANGUAGE"("id")
    ON DELETE NO ACTION
    ON UPDATE NO ACTION
    NOT DEFERRABLE
) WITHOUT OIDS;

CREATE INDEX "UNIT_idx_document" ON "public"."UNIT"
  USING btree ("fk_id_document");

CREATE INDEX "UNIT_text_idx" ON "public"."UNIT"
  USING hash ("text");

---

CREATE TABLE "public"."DOCUMENT" (
  "id" BIGINT NOT NULL, 
  "fk_id_job" BIGINT, 
  CONSTRAINT "DOCUMENT_pkey" PRIMARY KEY("id"), 
  CONSTRAINT "DOCUMENT_fk" FOREIGN KEY ("fk_id_job")
    REFERENCES "public"."JOB"("id")
    ON DELETE SET NULL
    ON UPDATE NO ACTION
    NOT DEFERRABLE   
) WITHOUT OIDS;

UPDATE: Database parameters

shared_buffers = 2048MB
effective_cache_size = 4096MB
work_mem = 32MB

Total memory: 32GB
CPU: Intel Xeon X3470 @ 2.93 GHz, 8MB cache

Answer 1

Here is an interesting part of the ANALYZE official documentation.

For large tables, ANALYZE takes a random sample of the table contents, rather than examining every row. [...] The extent of analysis can be controlled by adjusting the default_statistics_target configuration variable, or on a column-by-column basis by setting the per-column statistics target with ALTER TABLE ... ALTER COLUMN ... SET STATISTICS.

Apparently it is a common way to improve bad query plan. Analyze will be a bit slower, but query plan can be better.

ALTER TABLE