September 15, 2020

We present a new class of resizable sequential and concurrent hash map algorithms directed at both uni-processor and multicore machines. The new hopscotch. I am currently experimenting with various hash table algorithms, and I stumbled upon an approach called hopscotch hashing. Hopscotch. We present a new resizable sequential and concurrent hash map algorithm directed at both uniprocessor and multicore machines. The algorithm is based on a.

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Hopscotch hashing is a scheme in computer programming for resolving hash collisions of values of hash functions in a table using open addressing. Hi Emmanuel, If I read your ShadowHashMap code correctly, in lookup function you are linearly checking the whole neighborhood for the query key, which would include items that have a different key hash.

If neighborhoods are stored using linked lists, each bucket has a pointer to the next bucket in the same neighborhood.

All this sounds increasingly similar to Robin Hood Hashing. This also means that at any bucket, multiple neighborhoods are overlapping H to be exact.

The main idea behind hopscotch hashing is that each bucket has a neighborhood of size H. We hash b and get index 6. Bucket 0 is the initial bucket, and bucket 11 is the empty bucket found by linear probing.

Hopscotch Hashing

But in the end, my feeling is that with a densely filled hopscotch-hashing table, the exact neighborhood representation would not matter. Of course having such as large value would be useless, because it would be equivalent to using only linear probing with no reordering.

A great thing with the shadow representation is that the largest size of the neighborhood is theoretically the hopscitch of the hash table itself. This article is still missing an empirical study bashing would compare hopscotch hashing to other collision resolution methods. This can appear to be costly compared to just storing the neighborhoods, but actually if the size of the bucket array is a power of two, then the modulo can be computed using a bitwise AND, which is extremely fast.

However if the map reaches a point where removals and insertions are roughly balanced, then insertions will occur within deleted entries rather than null ones, while the nulls kind of naturally indicate the end of neighbourhood clusters. Regarding storing the hashed keys in the bucket array, the main advantage is for when the data is stored in secondary storage HDD, SSD, etc.


The desired property of the neighborhood is that the cost of finding an item in the buckets of the neighborhood is close to the cost of finding it in the bucket itself for example, by having buckets in the neighborhood fall within the same cache line.

But during my short experiments, it has been clear that using an increasing variable neighborhood size does not have any serious advantage over using a constant neighborhood size, at least for the goal of reaching higher load factors.

If the key does not match any of the keys for the entries in the neighborhood of the initial bucket, then the entry is simply not hashiing the table. Anyway at such high loads, the best thing to do would be to resize the table.

Hopscotch hashing is interesting because it guarantees a small number of look-ups to find entries. I just committed a fix, thanks for pointing it out!

Very Fast HashMap in C++: Hopscotch & Robin Hood Hashing (Part 1)

Neighborhood representations In the original paper, two representations of the neighborhoods were covered [2]. To speed the search, each bucket array entry includes a “hop-information” word, an H -bit bitmap that indicates which of the next H-1 entries contain items that hashed to the current entry’s virtual bucket. The original paper was mostly focusing on multi-core and concurrent environments.

Indeed, for the bitmap representation, the neighborhood of a bucket is determined using the bitmap stored with that bucket. This proof may create a misunderstanding, which is that the load factor can increase to very high values because hopscotch hashing will prevent clustering.

For each bucket, its neighborhood is a small collection of nearby consecutive buckets i. Another idea that I wanted to try was to have variable neighborhood sizes.

But this is not the case. For example if the implementation of a hash table needs to allow for resizing, then in some cases performance can be improved by storing the hashed keys. Implementation Variants Part 3: Your email address will never be published. This is a major improvement compared to basic open addressing that uses only probing.

This representation was not part of the original paper, this is just an idea that I wanted to experiment with. The algorithm uses a single array of n buckets. Show me the code. On way would be a linked list of offsets.


As a result, at most H consecutive look-ups will be required in contiguous memory locations, which is extremely cache friendly. My choice for hash function was the following: I am storing the hash hopscohch the key in each bucket, and my intent was to compare that stored hash with the hash of the key being looked up to avoid unnecessary accesses to the entry.

Assuming deletions have occurred in the table, if you have two buckets X and Y in the same linked list with a link from X to Y, there is no guarantee that Y will be stored at an address higher than X, and hopecotch, Y could be at an address lower than X. It is true that storing the hashed keys requires more memory, but hasbing avoids the need for extra memory to store the neighborhoods as it is the case with the bitmap and linked-list representations.

Hopscotch Hashing — Multicore Algorithmics – Multicore TAU group

The code from the paper implements two representations of the hopscotch hashing, the bitmap and the linked list [3]. Since the buckets in a same neighborhood will be found at a bounded distance, at most H-1small integers can be used to store offsets instead of larger and more costly addresses, which can save up a lot of memory.

A search can fail either because it finds an empty bucket or because it fails to find a bucket having the required initial bucket.

You probably have already seen it, but just in case, here is a link to another article in which I gathered more data for open-addressing hash tables, including hopscotch hashing: Lazy deletion leads to the apparition of large areas of buckets marked as deleted, that are unused but yet must be scanned through during look-ups, a phenomenon called contamination.

At this point, the state of the hash table is as shown prior to Step 1 in Figure 3.

First, a clear explanation of the insertion process is being given, which is independent from the representation of neighborhoods.