This is generally true, but there are some additional aspects.

1. With PostgreSQL heap, you need to access the heap page itself. And it's not for free. It goes all through the buffer manager and other related components.

2. In OrioleDB, we have a lightweight protocol to read from pages. In-memory pages are connected using direct links (https://www.orioledb.com/docs/architecture/overview#dual-poi...), and pages are read lock-less (https://www.orioledb.com/docs/architecture/overview#page-str...). Additionally, tree navigation for simple data types skips both copying and tuple deforming (https://www.orioledb.com/blog/orioledb-fastpath-search).

According to all of the above, I believe OrioleDB still wins in the case of secondary key lookup. I think this is indirectly confirmed by the results of the TPC-C benchmark, which contains quite a lot of log of secondary key lookups. However, this subject is worth dedicated benchmarking in the future.

It would be interesting to see how OrioleDB does with more OLAP-like loads. From when I spent a lot of time benchmarking this, the indirect index design was _the_ main reason why MySQL+InnoDB was losing significantly to Postgres on TPC-H (well, DBT-3).[1] There was a lot of working around it with covering indexes etc..

Of course, the flip side of the coin is that if you do an UPDATE of a row in the presence of a secondary index, and the UPDATE doesn't touch the key, then you don't need to update the index(es) at all. So it really depends on how much you update rows versus how often you index-scan them IME.

[1] TPC-H doesn't have difficult enough queries to really stress the planner, so it mattered comparatively less there than in other OLAP work.

Thank you, that would be on the TODO list.