Complexity of Error-Correcting Code Based on Nearest Neighbor Search Algorithm

The Nearest Neighbor search algorithm considered in this paper is well known (Elias algorithm). It uses error-correcting codes and constructs appropriate hash-coding schemas. These schemas preprocess the data in the form of lists. Each list is contained in some sphere, centered at a code-word. The algorithm is considered for the cases of perfect codes, so the spheres and, consequently, the lists do not intersect. As such codes exist for the limited set of parameters, the algorithm is considered for some other generalizations of perfect codes, and then the same data point may be contained in different lists. A formula of time complexity of the algorithm is obtained for these cases, using coset weight structures of the mentioned codes

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A nearest neighbor search algorithm for LR-LD on high SNR

2016 IEEE/ACIS 15th International Conference on Computer and Information Science (ICIS) ◽

10.1109/icis.2016.7550729 ◽

2016 ◽

Cited By ~ 1

Author(s):

Thae Thae Yu Khine ◽

Koji Araki ◽

Daisuke Mitsunaga ◽

Hua-An Zhao

Keyword(s):

Nearest Neighbor ◽

Search Algorithm ◽

Nearest Neighbor Search ◽

Neighbor Search

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Fast k-nearest neighbor search algorithm based on pyramid structure of wavelet transform and its application to texture classification

Digital Signal Processing ◽

10.1016/j.dsp.2009.10.011 ◽

2010 ◽

Vol 20 (3) ◽

pp. 837-845 ◽

Cited By ~ 9

Author(s):

Yu-Long Qiao ◽

Zhe-Ming Lu ◽

Jeng-Shyang Pan ◽

Sheng-He Sun

Keyword(s):

Wavelet Transform ◽

Nearest Neighbor ◽

Search Algorithm ◽

Texture Classification ◽

Nearest Neighbor Search ◽

K Nearest Neighbor ◽

Neighbor Search ◽

Pyramid Structure ◽

K Nearest Neighbor Search

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Fast document summarization using locality sensitive hashing and memory access efficient node ranking

International Journal of Electrical and Computer Engineering (IJECE) ◽

10.11591/ijece.v6i3.9030 ◽

2016 ◽

Vol 6 (3) ◽

pp. 945

Author(s):

Ercan Canhasi

Keyword(s):

Time Complexity ◽

Nearest Neighbor ◽

Linear Time ◽

Nearest Neighbor Search ◽

Memory Access ◽

Locality Sensitive Hashing ◽

Document Summarization ◽

Neighbor Search ◽

Node Ranking ◽

Similarity Graph

Text modeling and sentence selection are the fundamental steps of a typical extractive document summarization algorithm. The common text modeling method connects a pair of sentences based on their similarities. Even thought it can effectively represent the sentence similarity graph of given document(s) its big drawback is a large time complexity of $O(n^2)$, where n represents the number of sentences. The quadratic time complexity makes it impractical for large documents. In this paper we propose the fast approximation algorithms for the text modeling and the sentence selection. Our text modeling algorithm reduces the time complexity to near-linear time by rapidly finding the most similar sentences to form the sentences similarity graph. In doing so we utilized Locality-Sensitive Hashing, a fast algorithm for the approximate nearest neighbor search. For the sentence selection step we propose a simple memory-access-efficient node ranking method based on the idea of scanning sequentially only the neighborhood arrays. Experimentally, we show that sacrificing a rather small percentage of recall and precision in the quality of the produced summary can reduce the quadratic to sub-linear time complexity. We see the big potential of proposed method in text summarization for mobile devices and big text data summarization for internet of things on cloud. In our experiments, beside evaluating the presented method on the standard general and query multi-document summarization tasks, we also tested it on few alternative summarization tasks including general and query, timeline, and comparative summarization.

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