Abstract
Very recently, the unexpected combination of data structures and machine learning has led to the development of a new area of research, called learned data structures. Their distinguishing trait is the ability to reveal and exploit patterns and trends in the input data for achieving more efficiency in time and space, compared to previously known data structures. The goal of this chapter is to provide the first comprehensive survey of these results and to stimulate further research in this promising area.
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Notes
- 1.
We assume that universe \(\mathcal {U}\) is a range of reals because of the arithmetic operations required by the models. This works for any kind of keys that can be mapped to reals by preserving their order, such as integers or strings.
- 2.
Private correspondence with the authors clarified that only linear models were used in the hierarchy due to their superior performance.
- 3.
It has to be noted that a B+-tree supports also insertions and deletions, which require a more complex structure that is both slower and more space-inefficient than other static tree-based indexes.
- 4.
The authors suggest organising the buffer “like a hash table”. Even though hashing simplifies buffer modifications, we lose the ability to do predecessor or range queries efficiently.
- 5.
The authors do not discuss the details of this step, but we assume that it is performed in \(O(\log \tilde{m})\) time via a binary search on the \(\tilde{m}\) sorted key-model pairs.
- 6.
We remark that MurmurHash is a known function which can be implemented in a few dozen lines of C code.
- 7.
It has to be noted that for 5K elements a Bloom filter of \({\approx }6\) KB and \(k=7\) hash functions would have sufficed to achieve 1% false positives. Similarly, a Bloom filter of \({\approx }9\) KB and \(k=10\) hash functions would have sufficed to achieve 0.1% false positives.
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Acknowledgements
Part of this work has been supported by the Italian MIUR PRIN project “Multicriteria Data Structures and Algorithms: from compressed to learned indexes, and beyond” (Prot. 2017WR7SHH), by Regione Toscana (under POR FSE 2014/2020), and by the European Integrated Infrastructure for Social Mining and Big Data Analytics (SoBigData++, Grant Agreement # 871042).
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Ferragina, P., Vinciguerra, G. (2020). Learned Data Structures. In: Oneto, L., Navarin, N., Sperduti, A., Anguita, D. (eds) Recent Trends in Learning From Data. Studies in Computational Intelligence, vol 896. Springer, Cham. https://doi.org/10.1007/978-3-030-43883-8_2
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