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Register a new userAll-Purpose Hashing
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Added by
Guido Tagliavini
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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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 paper 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 to $1 - o(1)$ 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 $Theta(log n)$ bits, the space guarantees that Iceberg hashing offers, namely that is uses at most $log binom{|U|}{n} + O(n log log n)$ bits to store $n$ items from a universe $U$, 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.
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Recent years have seen more and more demand for a unified framework to address multiple realistic image retrieval tasks concerning both category and attributes. Considering the scale of modern datasets, hashing is favorable for its low complexity. However, most existing hashing methods are designed to preserve one single kind of similarity, thus improper for dealing with the different tasks simultaneously. To overcome this limitation, we propose a new hashing method, named Dual Purpose Hashing (DPH), which jointly preserves the category and attribute similarities by exploiting the Convolutional Neural Network (CNN) models to hierarchically capture the correlations between category and attributes. Since images with both category and attribute labels are scarce, our method is designed to take the abundant partially labelled images on the Internet as training inputs. With such a framework, the binary codes of new-coming images can be readily obtained by quantizing the network outputs of a binary-like layer, and the attributes can be recovered from the codes easily. Experiments on two large-scale datasets show that our dual purpose hash codes can achieve comparable or even better performance than those state-of-the-art methods specifically designed for each individual retrieval task, while being more compact than the compared methods.
A minimal perfect hash function bijectively maps a key set $S$ out of a universe $U$ into the first $|S|$ natural numbers. Minimal perfect hash functions are used, for example, to map irregularly-shaped keys, such as string, in a compact space so that metadata can then be simply stored in an array. While it is known that just $1.44$ bits per key are necessary to store a minimal perfect function, no published technique can go below $2$ bits per key in practice. We propose a new technique for storing minimal perfect hash functions with expected linear construction time and expected constant lookup time that makes it possible to build for the first time, for example, structures which need $1.56$ bits per key, that is, within $8.3$% of the lower bound, in less than $2$ ms per key. We show that instances of our construction are able to simultaneously beat the construction time, space usage and lookup time of the state-of-the-art data structure reaching $2$ bits per key. Moreover, we provide parameter choices giving structures which are competitive with alternative, larger-size data structures in terms of space and lookup time. The construction of our data structures can be easily parallelized or mapped on distributed computational units (e.g., within the MapReduce framework), and structures larger than the available RAM can be directly built in mass storage.
To get estimators that work within a certain error bound with high probability, a common strategy is to design one that works with constant probability, and then boost the probability using independent repetitions. Important examples of this approach are small space algorithms for estimating the number of distinct elements in a stream, or estimating the set similarity between large sets. Using standard strongly universal hashing to process each element, we get a sketch based estimator where the probability of a too large error is, say, 1/4. By performing $r$ independent repetitions and taking the median of the estimators, the error probability falls exponentially in $r$. However, running $r$ independent experiments increases the processing time by a factor $r$. Here we make the point that if we have a hash function with strong concentration bounds, then we get the same high probability bounds without any need for repetitions. Instead of $r$ independent sketches, we have a single sketch that is $r$ times bigger, so the total space is the same. However, we only apply a single hash function, so we save a factor $r$ in time, and the overall algorithms just get simpler. Fast practical hash functions with strong concentration bounds were recently proposed by Aamand em et al. (to appear in STOC 2020). Using their hashing schemes, the algorithms thus become very fast and practical, suitable for online processing of high volume data streams.
We present a novel hashing strategy for approximate furthest neighbor search that selects projection bases using the data distribution. This strategy leads to an algorithm, which we call DrusillaHash, that is able to outperform existing approximate furthest neighbor strategies. Our strategy is motivated by an empirical study of the behavior of the furthest neighbor search problem, which lends intuition for where our algorithm is most useful. We also present a variant of the algorithm that gives an absolute approximation guarantee; to our knowledge, this is the first such approximate furthest neighbor hashing approach to give such a guarantee. Performance studies indicate that DrusillaHash can achieve comparable levels of approximation to other algorithms while giving up to an order of magnitude speedup. An implementation is available in the mlpack machine learning library (found at http://www.mlpack.org).
We show a new proof for the load of obtained by a Cuckoo Hashing data structure. Our proof is arguably simpler than previous proofs and allows for new generalizations. The proof first appeared in Pinkas et. al. cite{PSWW19} in the context of a protocol for private set intersection. We present it here separately to improve its readability.
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