JAJacksonAllan·Nov 12, 2023
In my example the table stores the hash codes themselves instead of the keys (because the hash function is invertible)
Oh, I see, right. If determining the home bucket is trivial, then the back-shifting method is great. The issue is just that it’s not as much of a general-purpose solution as it may initially seem. In the bad cases, it's really bad.
With a different algorithm (Robin Hood or bidirectional linear probing), the load factor can be kept well over 90% with good performance, as the benchmarks in the same repo demonstrate.
I’ve seen the 90% claim made several times in literature on Robin Hood hash tables. In my experience, the claim is a bit exaggerated, although I suppose it depends on what our idea of “good performance” is. See these benchmarks, which again go up to a maximum load factor of 0.95 (although boost and Absl forcibly
Read the rest
grow/rehash at 0.85-0.9):
https://strong-starlight-4ea0ed.netlify.app/
Tsl, Martinus, and CC are all Robin Hood tables (https://github.com/Tessil/robin-map, https://github.com/martinus/robin-hood-hashing, and https://github.com/JacksonAllan/CC, respectively). Absl (from Google) and Boost are well-known C++ SIMD-based hash tables. Khash (https://github.com/attractivechaos/klib/blob/master/khash.h) is, I think, an ordinary open-addressing table using quadratic probing. Fastmap is a new, yet-to-be-published design that is fundamentally similar to bytell (https://www.youtube.com/watch?v=M2fKMP47slQ) but also incorporates some aspects of the aforementioned SIMD maps (in particular, it stores a 4-bit fragment of the hash code to avoid most false key comparisons).
As you can see, all the Robin Hood maps spike upwards dramatically as the load factor gets high, becoming as much as 5-6 times slower at 0.95 vs 0.5 in one of the benchmarks (uint64_t key, 256-bit struct value: Total time to erase 1000 existing elements with N elements in map). Only the SIMD maps (with Boost being the clear better performer of the two) and Fastmap appear mostly immune to load factor in all benchmarks, although the SIMD maps do - I believe - use tombstones for deletion in at least some cases.
I’ve only read briefly about bi-directional linear probing – never experimented with it.