Probabilistic Data Structures for Efficient Memory Use
Probabilistic data structures offer approximate answers to questions about data sets with significantly reduced memory usage. These structures are particularly useful in scenarios where exact precision is not required,…
Probabilistic data structures, such as Bloom filters, provide approximate answers to questions about data sets while significantly reducing memory usage. Unlike deterministic structures like sets and frequency tables, probabilistic structures may not deliver exact results but offer substantial space savings. For example, a Bloom filter can tell if an item is definitely not in the set or probably is, with the latter possibility being a false positive. A Bloom filter with 1,000,000 distinct 8-byte strings uses only 1.24 MB (about 10 bits per item), which is 50 times smaller than a regular set for the same data (Lobsters, 2023). [1]
The structure of a Bloom filter involves a large array of bits and multiple hash functions. When an item is added, k hash values are computed, and the corresponding bits are set. To check if an item is in the set, the same hash functions are applied, and if all the bits are set, the item is likely present, though not guaranteed. The use of a blocked Bloom filter improves cache efficiency by dividing the bit array into blocks that match the size of a CPU cache line, ensuring that each add or check operation only accesses one cache line (Lobsters, 2023). [1]
Count-min sketches are another type of probabilistic data structure that provides approximate frequency counts for items in a data set. These sketches trade accuracy for space and can be used in scenarios such as rate-limiting or caching decisions. For instance, a count-min sketch with estimates within 0.01% of the total count (with 99% probability) can be implemented using only 0.55 MB for 1,000,000 distinct 8-byte strings, which is 116 times smaller than a regular map (Lobsters, 2023). [1]
The research described in the arXiv paper was published on February 11, 2019, and is available as arXiv:1902.04023 [stat.CO]. The paper focuses on the development of on-line algorithms for computing approximations of rank-based statistics, particularly emphasizing accuracy near the tails of a distribution. It introduces a method that computes quantiles with relative accuracy proportional to $\max(q, 1-q)$, which is a significant departure from the absolute accuracy used in most other methods. This approach is especially effective in handling skewed distributions or ordered datasets without loss of accuracy when combining separately computed summaries. [3]
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The paper highlights the robustness of the algorithm with respect to skewed data and its ability to maintain accuracy when merging summaries. It also mentions the availability of an open-source Java implementation from the author, along with independent implementations in Go and Python. These implementations provide practical tools for applying the algorithm in different programming environments. The research has been cited in academic and technical contexts, indicating its relevance to data structures and algorithms in computational statistics. [3]
The paper is 22 pages long and includes 10 figures to illustrate the methodology and results. It is categorized under the subjects of computation (stat.CO) and data structures and algorithms (cs.DS). The submission history indicates that the paper was authored by Ted Dunning, who is affiliated with the research community in computational statistics. The paper's DOI is assigned by arXiv-issued DataCite, ensuring its formal citation in academic literature. [3]
Probabilistic data structures give you approximate answers to questions about the data they handle, such as whether a set contains a certain item or how many unique items are in a collection. Unlike deterministic structures like sets and frequency tables, the answers provided by probabilistic data structures might not be exact, but they allow for a drastic reduction in memory usage. For example, a regular set with 1,000,000 distinct 8-byte strings takes about 64 MB, whereas a Bloom filter for the same strings with a 1% false positive rate uses only 1.24 MB (about 10 bits per item) (source ID: 1). [1]
A Bloom filter is a set that trades certainty for space. It can tell you that an item is definitely not in the set, or that it probably is, which might be a false positive. The filter doesn't actually store the items, so it's much more compact than a regular set. The structure of a Bloom filter involves a large array of bits and multiple hash functions. To add an item, you compute k hash values for it and set the k bits at those positions (source ID: 1). [1]
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A count-min sketch is a frequency table that trades accuracy for space. It tells you approximately how many times each item has appeared. The estimate is never less than the actual count, but it can be higher. The sketch doesn't actually store the items, so it's much more compact than a regular map of per-item counts. For example, a regular map counting 1,000,000 distinct 8-byte strings takes about 64 MB, whereas a count-min sketch for the same strings with estimates within 0.01% of the total count (with 99% probability) uses only 0.55 MB (source ID: 1). [1]
Sources
Prepared with AI assistance from the cited sources.
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