scholarly journals List of Twin Clusters: A Data Structure for Similarity Joins in Metric Spaces

Author(s):  
Rodrigo Paredes ◽  
Nora Reyes
2012 ◽  
Vol 5 (12) ◽  
pp. 1922-1925 ◽  
Author(s):  
Yasin N. Silva ◽  
Spencer Pearson

2021 ◽  
Vol 12 (3) ◽  
Author(s):  
Leonardo Andrade Ribeiro ◽  
Felipe Ferreira Borges ◽  
Diego Oliveira

We consider the problem of efficiently answering set similarity joins on multi-attribute data. Traditional set similarity join algorithms assume string data represented by a single set and, thus, miss the opportunity to exploit predicates over multiple attributes to reduce the number of similarity computations. In this article, we present a framework to enhance existing algorithms with additional filters for dealing with multi-attribute data. We then instantiate this framework with a lightweight filtering technique based on a simple, yet effective data structure, for which exact and probabilistic implementations are evaluated. In this context, we devise a cost model to identify the best attribute ordering to reduce processing time. Moreover, alternative approaches are also investigated and a new algorithm combining key ideas from previous work is introduced. Finally, we present a thorough experimental evaluation, which demonstrates that our main proposal is efficient and significantly outperforms competing algorithms.


2020 ◽  
Vol 91 ◽  
pp. 101510 ◽  
Author(s):  
Sebastián Ferrada ◽  
Benjamin Bustos ◽  
Nora Reyes

Author(s):  
DANIELA MAFTULEAC

CAT(0) metric spaces and hyperbolic spaces play an important role in combinatorial and geometric group theory. In this paper, we present efficient algorithms for distance problems in CAT(0) planar complexes. First of all, we present an algorithm for answering single-point distance queries in a CAT(0) planar complex. Namely, we show that for a CAT(0) planar complex [Formula: see text] with n vertices, one can construct in O(n2 log n) time a data structure [Formula: see text] of size O(n2) so that, given a point [Formula: see text], the shortest path γ(x, y) between x and the query point y can be computed in linear time. Our second algorithm computes the convex hull of a finite set of points in a CAT(0) planar complex. This algorithm is based on Toussaint's algorithm for computing the convex hull of a finite set of points in a simple polygon and it constructs the convex hull of a set of k points in O(n2 log n + nk log k) time, using a data structure of size O(n2 + k).


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