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Title: A Linear-Time Algorithm and Analysis of Graph Relative Hausdorff Distance

Abstract

Graph similarity metrics serve far-ranging purposes across many domains in data science. As graph datasets grow in size, scientists need comparative tools that capture meaningful differences, yet are lightweight and scalable. Graph Relative Hausdorff (RH) distance is a promising, recently proposed measure for quantifying degree distribution similarity. In spite of recent interest in RH distance, little is known about its properties. Here, we conduct an algorithmic and analytic study of RH distance. In particular, we provide the first linear-time algorithm for computing RH distance, analyze examples of RH distance between families of graphs, and prove several analytic results concerning the range, density, and extremal behavior of RH distance values.

Authors:
 [1];  [1]; ORCiD logo [1]
  1. BATTELLE (PACIFIC NW LAB)
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1569008
Report Number(s):
PNNL-SA-141641
DOE Contract Number:  
AC05-76RL01830
Resource Type:
Journal Article
Journal Name:
SIAM Journal on Mathematics of Data Science
Additional Journal Information:
Journal Volume: 1; Journal Issue: 4
Country of Publication:
United States
Language:
English
Subject:
Relative Hausdorff distance, degree distribution, network science

Citation Formats

Aksoy, Sinan G., Nowak, Kathleen E., and Young, Stephen J. A Linear-Time Algorithm and Analysis of Graph Relative Hausdorff Distance. United States: N. p., 2019. Web. doi:10.1137/19M1248224.
Aksoy, Sinan G., Nowak, Kathleen E., & Young, Stephen J. A Linear-Time Algorithm and Analysis of Graph Relative Hausdorff Distance. United States. doi:10.1137/19M1248224.
Aksoy, Sinan G., Nowak, Kathleen E., and Young, Stephen J. Tue . "A Linear-Time Algorithm and Analysis of Graph Relative Hausdorff Distance". United States. doi:10.1137/19M1248224.
@article{osti_1569008,
title = {A Linear-Time Algorithm and Analysis of Graph Relative Hausdorff Distance},
author = {Aksoy, Sinan G. and Nowak, Kathleen E. and Young, Stephen J.},
abstractNote = {Graph similarity metrics serve far-ranging purposes across many domains in data science. As graph datasets grow in size, scientists need comparative tools that capture meaningful differences, yet are lightweight and scalable. Graph Relative Hausdorff (RH) distance is a promising, recently proposed measure for quantifying degree distribution similarity. In spite of recent interest in RH distance, little is known about its properties. Here, we conduct an algorithmic and analytic study of RH distance. In particular, we provide the first linear-time algorithm for computing RH distance, analyze examples of RH distance between families of graphs, and prove several analytic results concerning the range, density, and extremal behavior of RH distance values.},
doi = {10.1137/19M1248224},
journal = {SIAM Journal on Mathematics of Data Science},
number = 4,
volume = 1,
place = {United States},
year = {2019},
month = {10}
}