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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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This clustering bashing occurs around load factors of 0. This distinguishes it from linear probing which leaves the empty slot where it was found, possibly far away from the original bucket, or from cuckoo hashing that, in order to hopscotcn a free bucket, moves an item out of one of the desired buckets in the target arrays, and only then tries to find the displaced item a new place.

Here is my reasoning: The first step to retrieve an entry is to determine its initial bucket.

Hopscotch Hashing

Algorithms and Programming Business and Start-ups Random thoughts rants, product ideas, productivity, etc. In order to move the empty bucket E from the location where it was found into the neighborhood of B, it needs to be swapped with entries between the positions of B and E. Once we have the offset, we can use it as clever as robin hood hashing does: The neighborhood is thus a “virtual” bucket that has fixed size and overlaps with the next H-1 buckets.

Implementation Variants Part 3: From the hashed key only, it is possible to find for any entry the position of its initial bucket using the modulo operator. References [1] Submission draft for Hopscotch Hashing by Herlihy et at.

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. In the paper, one of the proofs states: The advantage of a bitmap or a linked list, as presented in the original paper, is that you only compare to keys of the items that landed in the same original bucket as the query key.

Consequently, the empty bucket E can be swapped with any of the preceding H-1 entries that have the position of E in their neighborhoods. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia has a nice representation: When using open addressing with only a probing sequence and no reordering, entries are inserted in the first empty buckets found in the sequence.


It is true that storing the hashed keys requires more memory, but it avoids the need for extra memory to store the neighborhoods as it is the case with the bitmap and linked-list representations. This is just a detail, but this will show up in the implementation and therefore it is something to keep in mind. This representation was not part of the original paper, this is just an idea that I wanted to experiment with.

Of course having such as large value would be useless, because it would be equivalent to using only linear probing with no reordering. 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 hopcsotch no guarantee that Y will be stored at an address higher than X, and indeed, Y could be at an address lower than X.

In addition, those look-ups are in contiguous memory areas, which is very cache friendly.

Hopscotch hashing – Wikipedia

Hopscotch After contemplating a while, I have come to the conclusion that Hopscotch is just a bad version of Robin Hood Hashing. To remove an item from the table, one simply removes it from the table entry.

The idea is that holscotch hashing “moves the empty slot hashinv the desired bucket”. An advantage of using linked lists is that the size of the neighborhoods can be much larger without too much overhead on the total size of the bucket array.

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. Note that the Hopscotch insertion algorithm discussed in Section 2. 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.

The third search is confined to the neighborhood of bucket 6 and hence will terminate at or before bucket 9. The main drawback of using bitmaps is that the maximum size of the neighborhoods is limited by the number of bits in the bitmaps.

Instead, I am presenting the insertion process of hopscotch hashing with a diagram, in Figure 1 below. As the table fills up, this prevents the lookup method from doing many random reads on the secondary storage, which are costly.

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

Unfortunately, linked lists are not very cache friendly. If neighborhoods are stored using linked lists, each bucket has a pointer to the next bucket in the same neighborhood. Storing the hashed keys is frequently required. Proceedings of the 22nd international symposium on Distributed Computing. 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 hashlng the current bucket.


Hopscotch hashing was introduced by Herlihy et al. For a perfectly full hashmap, where each bucket contains a corresponding entry, of the 32 hop bits there will be just a single bit that is set to 1. If no empty bucket is found, the insertion algorithm is terminated automatically after it has inspected a predetermined number of buckets.

However, this does not prevent multiple nopscotch to cluster the overlapping area of their respective neighborhoods. Since it is taken by something else, it will have a higher value, so we are certain this is not the bucket we are looking for.

At index 8 we expect an offset 2 if it contains an element that was indexed to 6. After spending some time optimizing, I am mostly happy with the results. 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 hashng within the same cache line.

Hopscotch Hashing — Multicore Algorithmics – Multicore TAU group

I am storing the hash of 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. At this point, the state of the hash table hashkng as shown prior to Step 1 in Figure 3.

Anyway at such high loads, the best thing to do would be to resize the table. Figure 2 below shows the hash table presented in Figure 1, and along with it the bitmaps for each of the buckets.

If the second option is true, this would mean that the experimental hahing presented in the paper were not obtained using hopscotch hashing, and therefore that the conclusions reached by this paper could hshing be taken seriously.