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Is there a way to optimize this UPDATE command to run faster?
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I agree. And we can go even further: make the table WITHOUT ROWID, so the engine will use a single Btree

 CREATE TABLE SnapshotParameters(
     snapshot_id   integer,
     object_id     integer,
     param_id      integer,
     param_value   integer,
     PRIMARY KEY(snapshot_id, object_id, param_id)
 ) WITHOUT ROWID
 
 No external indexes needed