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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Nevertheless, with this code I was able to find out more about the practical behavior of hopscotch hashing, and some of the limitations that were not described in the original paper. Instead, I am presenting the insertion process of hopscotch hashing with a diagram, in Figure 1 below. Unfortunately, linked lists are not very cache friendly. If the neighborhood buckets are cache aligned, then one could apply a reorganization operation in which items are moved into the now vacant location in order to improve alignment.

In order to insert a new entry, its key is hashed to find the initial bucket for the entry, denoted as B.

One advantage of hopscotch hashing is that it provides good performance at very high table load factors, even ones exceeding 0. My intuition was that by starting with smaller neighborhood sizes, items would hopscptch more spatially localized, which would allow for higher load factors to be reached than with constant neighborhood sizes.

Hopscotch Hashing

Conclusion This was just a short presentation of hopscotch hashing. Robin Hood Hashing vs.

The original paper was using the bitmap representation to present the algorithm, and I believe that hopscotcg are simpler without it. On way would be a linked list of offsets. Due to the hopscotch method, an entry may not be in the bucket it was hashed to, its initial bucket, but most likely in a bucket in the neighborhood of its initial bucket. Here is a comparison table best values bold.

The hhopscotch uses a single array of n buckets.

Hopscotch hashing | Code Capsule

After spending some time optimizing, I am mostly happy with the results. From the hashed key only, it is possible to find for any gopscotch the position of its initial bucket using the modulo operator. If the entry were saved there, subsequent trials to retrieve it would fail, because the search would be bounded to the neighborhood of B.


With these insights, I believe I have a great idea to implement a highly efficient variant of the robin hood hash table, that takes some ideas from the hopscotch implementation. This was just a short presentation of hopscotch hashing.

From there, the neighborhood to which the entry belongs can be determined, which is the initial bucket that was just derived and the next H-1 buckets. At this point, I believe that long paragraphs of explanations would not be of any help. So the above example from a could be stored like this: Neighborhoods can be stored using bitmaps bit arrays.

The offset at hopscotfh 6 is 0: The bitmap for bucket 5 is thereforewith a bit set hopdcotch 1 at index 1, because bucket 6 is at an offset of 1 from bucket 5. Hopscotch hashing is interesting because it guarantees a small number of look-ups to find entries. 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.

Even by scanning only 1 out of 5 or 6 buckets in a neighborhood, the number of cache lines that would be loaded in the L1 cache would be roughly the same for all neighborhood representations, and there would be little difference in performance between them assuming byte L1 cache lines.

Retrieved from ” https: The code from the paper implements two representations of the hopscotch hashing, the bitmap and the linked list [3]. By using this site, you agree to the Terms of Use and Privacy Policy. The fourth search finds empty bucket 9 and terminates.

Hopscotch Hashing — Multicore Algorithmics – Multicore TAU group

To remove an item from the table, one simply removes it from the table entry. And larger neighborhoods can be useful to allow for more entries to be hopsscotch in the hash table, and reach higher load factors. The first search is confined to the neighborhood of bucket 3 and hence will terminate at or before bucket 6, given that the neighborhood size H equals 4. The main drawback of using bitmaps is that the maximum size of the neighborhoods is limited by the number of bits hasning the bitmaps.


The major limitation of hopscotch hashing is that the load factor does not increase as described in the original paper.

I am using Visual Studio Update 3, 64 bit, Intel i 3. We hash b and get index 6. On the other hand, a successful search will always initiate another search. So now we can ditch the hop size, and just keep swapping elements exactly like robin hood hashing does.

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

That means at index 6 is an element that actually belongs there: The original paper was mostly focusing on multi-core and concurrent environments. This is just a detail, but this will show up in the implementation and therefore it is something to keep in mind. From what I understand from the code, it appears that putIfAbsent is just implementing a linear probing and that buckets are then linked together to prevent probing all buckets when calling containsKey. 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: Each bit in that bitmap indicates if the current bucket or one of its following H-1 buckets are holding an entry which belongs to the neighborhood of the current bucket.

I found a typing error in the last part of the second line in section 2.

Storing the hashed keys is frequently required. Home About Me Keto Calculator.

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