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Despite being one of the oldest data structures in computer science, hash tables continue to be the focus of a great deal of both theoretical and empirical research. A central reason for this is that many of the fundamental properties that one desires from a hash table are difficult to achieve simultaneously; thus many variants offering different trade-offs have been proposed.

This article introduces Iceberg hashing, a hash table that simultaneously offers the strongest known guarantees on a large number of core properties. Iceberg hashing supports constant-time operations while improving on the state of the art for space efficiency, cache efficiency, and low failure probability. Iceberg hashing is also the first hash table to support a load factor of up to1 - o(1)while being stable, meaning that the position where an element is stored only ever changes when resizes occur. In fact, in the setting where keys are Θ (logn) bits, the space guarantees that Iceberg hashing offers, namely that it uses at most\(\log \binom{|U|}{n} + O(n \log \ \text{log} n)\)bits to storenitems from a universeU, matches a lower bound by Demaine et al. that applies to any stable hash table.

Iceberg hashing introduces new general-purpose techniques for some of the most basic aspects of hash-table design. Notably, our indirection-free technique for dynamic resizing, which we call waterfall addressing, and our techniques for achieving stability and very-high probability guarantees, can be applied to any hash table that makes use of the front-yard/backyard paradigm for hash table design.

 

We present IronSync, an automated verification framework for concurrent code with shared memory. IronSync scales to complex systems by splitting system-wide proofs into isolated concerns such that each can be substantially automated. As a starting point, IronSync’s ownership type system allows a developer to straightforwardly prove both data safety and the logical correctness of thread-local operations. IronSync then introduces the concept of a Localized Transition System, which connects the correctness of local actions to the correctness of the entire system. We demonstrate IronSync by verifying two state-of-the-art concurrent systems comprising thousands of lines: a library for black-box replication on NUMA architectures, and a highly concurrent page cache. 

Storage devices have complex performance profiles, including costs to initiate IOs (e.g., seek times in hard drives), parallelism and bank conflicts (in SSDs), costs to transfer data, and firmware-internal operations. The Disk-access Machine (DAM) model simplifies reality by assuming that storage devices transfer data in blocks of size B and that all transfers have unit cost. Despite its simplifications, the DAM model is reasonably accurate. In fact, if B is set to the half-bandwidth point, where the latency and bandwidth of the hardware are equal, then the DAM approximates the IO cost on any hardware to within a factor of 2. Furthermore, the DAM model explains the popularity of B-trees in the 1970s and the current popularity of B ɛ -trees and log-structured merge trees. But it fails to explain why some B-trees use small nodes, whereas all B ɛ -trees use large nodes. In a DAM, all IOs, and hence all nodes, are the same size. In this article, we show that the affine and PDAM models, which are small refinements of the DAM model, yield a surprisingly large improvement in predictability without sacrificing ease of use. We present benchmarks on a large collection of storage devices showing that the affine and PDAM models give good approximations of the performance characteristics of hard drives and SSDs, respectively. We show that the affine model explains node-size choices in B-trees and B ɛ -trees. Furthermore, the models predict that B-trees are highly sensitive to variations in the node size, whereas B ɛ -trees are much less sensitive. These predictions are born out empirically. Finally, we show that in both the affine and PDAM models, it pays to organize data structures to exploit varying IO size. In the affine model, B ɛ -trees can be optimized so that all operations are simultaneously optimal, even up to lower-order terms. In the PDAM model, B ɛ -trees (or B-trees) can be organized so that both sequential and concurrent workloads are handled efficiently. We conclude that the DAM model is useful as a first cut when designing or analyzing an algorithm or data structure but the affine and PDAM models enable the algorithm designer to optimize parameter choices and fill in design details. 

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.