Standard Vs Uniform Binary Search and Their Variants in Learned Static Indexing: The Case of the Searching on Sorted Data Benchmarking Software Platform
Universitá degli Studi di Palermo（巴勒莫大学）
Domenico Amato, Giosuè Lo Bosco, Raffaele Giancarlo
备注：
arXiv admin note: substantial text overlap with arXiv:2107.09480
Learned Indexes are a novel approach to search in a sorted table. A model is used to predict an interval in which to search into and a Binary Search routine is used to finalize the search. They are quite effective. For the final stage, usually, the lower_bound routine of the Standard C++ library is used, although this is more of a natural choice rather than a requirement. However, recent studies, that do not use Machine Learning predictions, indicate that other implementations of Binary Search or variants, namely k-ary Search, are better suited to take advantage of the features offered by modern computer architectures. With the use of the Searching on Sorted Sets SOSD Learned Indexing benchmarking software, we investigate how to choose a Search routine for the final stage of searching in a Learned Index. Our results provide indications that better choices than the lower_bound routine can be made. We also highlight how such a choice may be dependent on the computer architecture that is to be used. Overall, our findings provide new and much-needed guidelines for the selection of the Search routine within the Learned Indexing framework.
Machine Learning Techniques, properly combined with Data Structures, have resulted in Learned Static Indexes, innovative and powerful tools that speed-up Binary Search, with the use of additional space with respect to the table being searched into. Such space is devoted to the Machine Learning Model. Although in their infancy, they are methodologically and practically important, due to the pervasiveness of Sorted Table Search procedures. In modern applications, model space is a key factor and, in fact, a major open question concerning this area is to assess to what extent one can enjoy the spe…
Lattice data structures are space efficient and cache-suitable data structures. The basic searching, insertion, and deletion operations are of time complexity $O(\sqrt{N})$. We give a jump searching algorithm of time complexity $O(J(L)\log(N))$, where $J(L)$ is the jump factor of the lattice. $J(L)$ approaches $4$ when the degree of sortedness of the lattice approaches $\sqrt{N}$. A sorting procedure of time complexity $O(\sqrt{N})$ that can be used, during the system idle time, to increase the degree of sortedness of the lattice is given.
We examine the problem of searching sequentially for a desired real value (a key) within a sorted unbalanced three-dimensional finite real array. This classic problem can be viewed as determining the correct dimensional threshold function from a finite class of such functions within the array, based on sequential queries that take the form of point samples. This note addresses the challenge of constructing algorithms that require the minimum number of queries necessary in the worst case, to search for a given key in arrays that have three dimensions with sizes that are not necessarily equal.
The rapid advance of DNA sequencing technologies has yielded databases of thousands of genomes. To search and index these databases effectively, it is important that we take advantage of the similarity between those genomes. Several authors have recently suggested searching or indexing only one reference genome and the parts of the other genomes where they differ. In this paper we survey the twenty-year history of this idea and discuss its relation to kernelization in parameterized complexity.
Text indexing, the problem in which one desires to preprocess a (usually large) text for future (shorter) queries, has been researched ever since the suffix tree was invented in the early 70's. With textual data continuing to increase and with changes in the way it is accessed, new data structures and new algorithmic methods are continuously required. Therefore, text indexing is of utmost importance and is a very active research domain. Orthogonal range searching, classically associated with the computational geometry community, is one of the tools that has increasingly become important for va…
Strings form a fundamental data type in computer systems. String searching has been extensively studied since the inception of computer science. Increasingly many applications have to deal with imprecise strings or strings with fuzzy information in them. String matching becomes a probabilistic event when a string contains uncertainty, i.e. each position of the string can have different probable characters with associated probability of occurrence for each character. Such uncertain strings are prevalent in various applications such as biological sequence data, event monitoring and automatic ECG…
We revisit the classical algorithms for searching over sorted sets to introduce an algorithm refinement, called Adaptive Search, that combines the good features of Interpolation search and those of Binary search. W.r.t. Interpolation search, only a constant number of extra comparisons is introduced. Yet, under diverse input data distributions our algorithm shows costs comparable to that of Interpolation search, i.e., O(log log n) while the worst-case cost is always in O(log n), as with Binary search. On benchmarks drawn from large datasets, both synthetic and real-life, Adaptive search scores …
We introduce the first index that can be built in $o(n)$ time for a text of length $n$, and can also be queried in $o(q)$ time for a pattern of length $q$. On an alphabet of size $σ$, our index uses $O(n\sqrt{\log n\logσ})$ bits, is built in $O(n((\log\log n)^2+\sqrt{\logσ})/\sqrt{\log_σn})$ deterministic time, and computes the number $\mathrm{occ}$ of occurrences of the pattern in time $O(q/\log_σn+\log n)$. Each such occurrence can then be found in $O(\sqrt{\log n\logσ})$ time. By slightly increasing the space and construction time, to $O(n(\sqrt{\log n\logσ}+ \logσ\log^\varepsilon n))$ and …
Data management applications store their data using structured files in which data are usually sorted to serve indexing and queries. However, in-place insertions and removals of data are not naturally supported in a file's address space. To avoid repeatedly rewriting existing data in a sorted file to admit changes in place, applications usually employ extra layers of indirections, such as mapping tables and logs, to admit changes out of place. However, this approach leads to increased access cost and excessive complexity. This paper presents a novel storage engine that provides a flexible addr…
We attempt to determine the best order and search algorithm to store $n$ comparable data items in an array, $A$, of length $n$ so that we can, for any query value, $x$, quickly find the smallest value in $A$ that is greater than or equal to $x$. In particular, we consider the important case where there are many such queries to the same array, $A$, which resides entirely in RAM. In addition to the obvious sorted order/binary search combination we consider the Eytzinger (BFS) layout normally used for heaps, an implicit B-tree layout that generalizes the Eytzinger layout, and the van Emde Boas la…
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Given an array $X$ of $N+1$ strictly ordered floating point numbers and a floating point number $z$ in the interval $[X_0,X_N)$, a common problem is to find the index $i$ of the interval $[X_{i},X_{i+1})$ containing $z$. This problem arises for instance in the context of spline interpolation or the computation of empirical probability distribution from empirical data. Often it needs to be solved for a large number of different values $z$ and the same array $X$, which makes it worth investing resources upfront in pre-processing the array $X$ with the goal of speeding up subsequent search operat…
In this paper, we present a framework based on a simple data structure and parameterized algorithms for the problems of finding items in an unsorted list of linearly ordered items based on their rank (selection) or value (search). As a side-effect of answering these online selection and search queries, we progressively sort the list. Our algorithms are based on Hoare's Quickselect, and are parameterized based on the pivot selection method. For example, if we choose the pivot as the last item in a subinterval, our framework yields algorithms that will answer q<=n unique selection and/or search …
Luleå University of Technology（吕勒奥理工大学）；Gavagai AB（Gavagai公司）
We present an incremental, scalable and efficient dimension reduction technique for tensors that is based on sparse random linear coding. Data is stored in a compactified representation with fixed size, which makes memory requirements low and predictable. Component encoding and decoding are performed on-line without computationally expensive re-analysis of the data set. The range of tensor indices can be extended dynamically without modifying the component representation. This idea originates from a mathematical model of semantic memory and a method known as random indexing in natural language…
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