Dynamic interpolation search

Mehlhorn, Kurt; Tsakalidis, Athanasios K.

doi:10.1007/bfb0015768

Cited by 16 publications

(37 citation statements)

References 7 publications

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“…Interpolation search faces the limitation that as the distribution varies from the assumption of a linear scale, the algorithm starts to fail and reaches a worst-case complexity of O (n), which is same as linear search. Interpolation search tree [14] data structure has been introduced with an average cost of O (log (log n)) for search operations and a worst case cost of O (log ~ n) to overcome the above drawback. The augmented sampled forest, or ASF [15] was introduced by Arne Andersson and Christer Mattsson to support a large class of distributions using a dynamic approach.…”

Section: Interpolation Searchmentioning

confidence: 99%

Equipartition Search a New Algorithm for Searching

Agarwal¹,

Gakhar²,

Thakur³

2016

IJCA

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Searching finds wide application in computer systems and till date, it remains one of the most fundamental operation. The need for evolving searching algorithm is never ending. This paper focuses on proposing a new algorithm namely Equipartition search algorithm and compares this method to existing methods by searching in various sequences. Results have been compiled by taking running time as a major parameter. As evident from the results, the Equipartition search method performs better than compared algorithms for several distributions. Hence the proposed method helps to reduce the running time in searching operation.

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Section: Interpolation Searchmentioning

confidence: 99%

Equipartition Search a New Algorithm for Searching

Agarwal¹,

Gakhar²,

Thakur³

2016

IJCA

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“…Given two functions f 1 and f 2 , a density function [30,4] if there exists a constant β, such that for all c 1 , c 2 , c 3 , a ≤ c 1 < c 2 < c 3 ≤ b, and all integers n, it holds that: = O( 1 f1 ); that is, f 1 measures how fine is the partitioning of an arbitrary subinterval. Function f 2 guarantees that no part, of the f 1 possible, gets more probability mass than β·f2 n ; that is, f 2 measures the sparseness of any subinterval [c 2 − c3−c1 f1 , c 2 ] ⊆ [c 1 , c 3 ].…”

Section: Probability Distributionsmentioning

confidence: 99%

Dynamic 3-sided planar range queries with expected doubly-logarithmic time

Brodal

Kaporis

Papadopoulos

et al. 2014

Theoretical Computer Science

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Abstract. We consider the problem of maintaining dynamically a set of points in the plane and supporting range queries of the type [a, b] × (−∞, c]. We assume that the inserted points have their x-coordinates drawn from a class of smooth distributions, whereas the y-coordinates are arbitrarily distributed. The points to be deleted are selected uniformly at random among the inserted points. For the RAM model, we present a linear space data structure that supports queries in O(log log n + t) expected time with high probability and updates in O(log log n) expected amortized time, where n is the number of points stored and t is the size of the output of the query. For the I/O model we support queries in O(log log B n + t/B) expected I/Os with high probability and updates in O(log B log n) expected amortized I/Os using linear space, where B is the disk block size. The data structures are deterministic and the expectation is with respect to the input distribution.

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“…However, none of these works consider the trees that could have lower than logarithmic height under a wide range of distributions. In this work, we consider the parallel batched version of Interpolation Search Tree (later called IST) introduced in [7]. The main difference with the previously researched data structures is that insertions, deletions and searches with smoothly distributed arguments take (log log ) time, where is the size of the tree.…”

mentioning

confidence: 99%

Parallel Batched Interpolation Search Tree

Aksenov,

Kokorin,

Martsenyuk

2021

Preprint

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Ordered set (and map) is one of the most used data type. In addition to standard set operations, like insert, delete and contains, it can provide set-set operations such as union, intersection, and difference. Each of these set-set operations is equivalent to batched operations: the data structure should process a set of operations insert, delete and contains. It is obvious that we want these "large" operations to be parallelized. Typically, these sets are implemented with the trees of logarithmic height, such as 2-3 tree, Treap, AVL tree, Red-Black tree, etc. Until now, little attention was devoted to data structures that work better but under several restrictions on the data. In this work, we parallelize Interpolation Search Tree which serves each request from a smooth distribution in doubly-logarithmic time. Our data structure of size performs a batch of operations in ( log log ) work and poly-log span.

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Dynamic interpolation search

Cited by 16 publications

References 7 publications

Equipartition Search a New Algorithm for Searching

Equipartition Search a New Algorithm for Searching

Dynamic 3-sided planar range queries with expected doubly-logarithmic time

Parallel Batched Interpolation Search Tree

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