An Extension of the Das and Mathieu QPTAS to the Case of Polylog Capacity Constrained CVRP in Metric Spaces of a Fixed Doubling Dimension

2020 ◽  
pp. 49-68
Author(s):  
Michael Khachay ◽  
Yuri Ogorodnikov ◽  
Daniel Khachay
Keyword(s):  
Metric Spaces ◽  
Doubling Dimension ◽  
Capacity Constrained

scholarly journals MapReduce and streaming algorithms for diversity maximization in metric spaces of bounded doubling dimension

2017 ◽  
Vol 10 (5) ◽  
pp. 469-480 ◽  
Author(s):  
Matteo Ceccarello ◽  
Andrea Pietracaprina ◽  
Geppino Pucci ◽  
Eli Upfal
Keyword(s):  
Metric Spaces ◽  
Streaming Algorithms ◽  
Doubling Dimension

scholarly journals Low-interference networks in metric spaces of bounded doubling dimension

2011 ◽  
Vol 111 (23-24) ◽  
pp. 1120-1123 ◽  
Author(s):  
Anil Maheshwari ◽  
Michiel Smid ◽  
Norbert Zeh
Keyword(s):  
Metric Spaces ◽  
Doubling Dimension ◽  
Interference Networks

scholarly journals On Metric DBSCAN with Low Doubling Dimension

2020 ◽  
Author(s):  
Hu Ding ◽  
Fan Yang ◽  
Mingyue Wang
Keyword(s):  
Euclidean Space ◽  
Metric Spaces ◽  
Spatial Clustering ◽  
High Dimensional ◽  
Dimensional Euclidean Space ◽  
Index Structures ◽  
Doubling Dimension ◽  
Density Based Clustering ◽  
Speed Up ◽  
Low Dimensional

The density based clustering method Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is a popular method for outlier recognition and has received tremendous attention from many different areas. A major issue of the original DBSCAN is that the time complexity could be as large as quadratic. Most of existing DBSCAN algorithms focus on developing efficient index structures to speed up the procedure in low-dimensional Euclidean space. However, the research of DBSCAN in high-dimensional Euclidean space or general metric spaces is still quite limited, to the best of our knowledge. In this paper, we consider the metric DBSCAN problem under the assumption that the inliers (excluding the outliers) have a low doubling dimension. We apply a novel randomized k-center clustering idea to reduce the complexity of range query, which is the most time consuming step in the whole DBSCAN procedure. Our proposed algorithms do not need to build any complicated data structures and are easy to implement in practice. The experimental results show that our algorithms can significantly outperform the existing DBSCAN algorithms in terms of running time.

Crystallography in two-dimensional metric spaces*

1969 ◽  
Vol 130 (1-6) ◽  
pp. 277-303 ◽  
Author(s):  
Aloysio Janner ◽  
Edgar Ascher
Keyword(s):  
Metric Spaces ◽  
Two Dimensional

Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem

2016 ◽  
Vol 2017 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Muhammad Usman Ali ◽  
◽  
Tayyab Kamran ◽  
Mihai Postolache ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Integral Inclusion

ON THE QUANTIFICATION OF UNIFORM PROPERTIES.PART 2

2001 ◽  
Vol 37 (1-2) ◽  
pp. 169-184
Author(s):  
B. Windels
Keyword(s):  
Metric Spaces ◽  
Uniform Spaces ◽  
Complete Metric Spaces ◽  
The Subject

In 1930 Kuratowski introduced the measure of non-compactness for complete metric spaces in order to measure the discrepancy a set may have from being compact.Since then several variants and generalizations concerning quanti .cation of topological and uniform properties have been studied.The introduction of approach uniform spaces,establishes a unifying setting which allows for a canonical quanti .cation of uniform concepts,such as completeness,which is the subject of this article.

Sign in / Sign up

Export Citation Format

Share Document