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We revisit the problem of building static hash tables on the GPU and present an efficient implementation of bucketed hash tables. By decoupling the probing scheme from the hash table in-memory representation, we offer an implementation where the number of probes and the bucket size are the only factors limiting performance. Our analysis sweeps through the hash table parameter space for two probing schemes: cuckoo and iceberg hashing. We show that a bucketed cuckoo hash table (BCHT) that uses three hash functions outperforms alternative methods that use iceberg hashing and a cuckoo hash table that uses a bucket size of one. At load factors as high as 0.99, BCHT enjoys an average probe count of 1.43 during insertion. Using three hash functions only, positive and negative queries require at most 1.39 and 2.8 average probes per key, respectively.
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Efficient Usage of One-Sided RDMA for Linear Probing
RDMA has been an important building block for many high-performance distributed key-value stores in recent prior work. To sustain millions of operations per second per node, many of these works use hashing schemes, such as cuckoo hashing, that guarantee that an existing key can be found in a small, constant number of RDMA operations. In this paper, we explore whether linear probing is a compelling design alternative to cuckoo-based hashing schemes. Instead of reading a fixed number of bytes per RDMA request, this paper introduces a mathematical model that picks the optimal read size by balancing the cost of performing an RDMA operation with the probability of encountering a probe sequence of a certain length. The model can further leverage optimization hints about the location of clusters of keys, which commonly occur in skewed key distributions. We extensively evaluate the performance of linear probing with a variable read size in a modern cluster to understand the trade-offs between cuckoo hashing and linear probing. We find that cuckoo hashing outperforms linear probing only in very highly loaded hash tables (load factors at 90% or higher) that would be prohibitively expensive to maintain in practice. Overall, linear probing with variable-sized reads using our model has up to 2.8× higher throughput than cuckoo hashing, with throughput as high as 50M lookup operations per second per node.
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- Award ID(s):
- 1816577
- PAR ID:
- 10277026
- Date Published:
- Journal Name:
- Eleventh International Workshop on Accelerating Analytics and Data Management Systems Using Modern Processor and Storage Architectures (AMDS'20)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Hashing is a fundamental operation in database management, playing a key role in the implementation of numerous core database data structures and algorithms. Traditional hash functions aim to mimic a function that maps a key to a random value, which can result in collisions, where multiple keys are mapped to the same value. There are many well-known schemes like chaining, probing, and cuckoo hashing to handle collisions. In this work, we aim to study if using learned models instead of traditional hash functions can reduce collisions and whether such a reduction translates to improved performance, particularly for indexing and joins. We show that learned models reduce collisions in some cases, which depend on how the data is distributed. To evaluate the effectiveness of learned models as hash function, we test them with bucket chaining, linear probing, and cuckoo hash tables. We find that learned models can (1) yield a 1.4x lower probe latency, and (2) reduce the non-partitioned hash join runtime with 28% over the next best baseline for certain datasets. On the other hand, if the data distribution is not suitable, we either do not see gains or see worse performance. In summary, we find that learned models can indeed outperform hash functions, but only for certain data distributions.more » « less
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Today’s filters, such as quotient, cuckoo, and Morton, have a trade-off between space and speed; even when moderately full (e.g., 50%-75% full), their performance degrades nontrivially. The result is that today’s systems designers are forced to choose between speed and space usage. In this paper, we present the vector quotient filter (VQF). Locally, the VQF is based on Robin Hood hashing, like the quotient filter, but uses power-of-two-choices hashing to reduce the variance of runs, and thus others consistent, high throughput across load factors. Power-of-two-choices hashing also makes it more amenable to concurrent updates, compared to the cuckoo filter and variants. Finally, the vector quotient filter is designed to exploit SIMD instructions so that all operations have $ (1) cost, independent of the size of the filter or its load factor. We show that the vector quotient flter is 2x faster for inserts compared to the Morton filter (a cuckoo filter variant and state-of- the-art for inserts) and has similar lookup and deletion performance as the cuckoo filter (which is fastest for queries and deletes), despite having a simpler design and implementation. The vector quotient filter has minimal performance decline at high load factors, a problem that has plagued modern filters, including quotient, cuckoo, and Morton. Furthermore, we give a thread-safe version of the vector quotient filter and show that insertion throughput scales 3x with four threads compared to a single thread.more » « less
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First introduced in 1954, the linear-probing hash table is among the oldest data structures in computer science, and thanks to its unrivaled data locality, linear probing continues to be one of the fastest hash tables in practice. It is widely believed and taught, however, that linear probing should never be used at high load factors; this is because of an effect known as primary clustering which causes insertions at a load factor of 1 - 1/x to take expected time O(x2) (rather than the intuitive running time of ⇥(x)). The dangers of primary clustering, first discovered by Knuth in 1963, have now been taught to generations of computer scientists, and have influenced the design of some of the most widely used hash tables in production. We show that primary clustering is not the foregone conclusion that it is reputed to be. We demonstrate that seemingly small design decisions in how deletions are implemented have dramatic effects on the asymptotic performance of insertions: if these design decisions are made correctly, then even if a hash table operates continuously at a load factor of 1 - (1/x), the expected amortized cost per insertion/deletion is O(x). This is because the tombstones left behind by deletions can actually cause an anti-clustering effect that combats primary clustering. Interestingly, these design decisions, despite their remarkable effects, have historically been viewed as simply implementation-level engineering choices. We also present a new variant of linear probing (which we call graveyard hashing) that completely eliminates primary clustering on any sequence of operations: if, when an operation is performed, the current load factor is 1 1/x for some x, then the expected cost of the operation is O(x). Thus we can achieve the data locality of traditional linear probing without any of the disadvantages of primary clustering. One corollary is that, in the external-memory model with a data blocks of size B, graveyard hashing offers the following remarkably strong guarantee: at any load factor 1 1/x satisfying x = o(B), graveyard hashing achieves 1 + o(1) expected block transfers per operation. In contrast, past external-memory hash tables have only been able to offer a 1 + o(1) guarantee when the block size B is at least O(x2). Our results come with actionable lessons for both theoreticians and practitioners, in particular, that well- designed use of tombstones can completely change the asymptotic landscape of how the linear probing behaves (and even in workloads without deletions).more » « less
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