Approximation algorithms for min-distance problems
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LIPIcs-ICALP-2019-46.pdf
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Published version
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518.5 KB
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Checksum (MD5)
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Author(s)
Williams, Virginia Vassilevska
Wein, Nicole
Dalirrooyfard, Mina
Vyas, Nikhil
Xu, Yinzhan
Yu, Yuancheng
Date Issued
2019
Journal
Leibniz International Proceedings in Informatics, LIPIcs
Citation
Williams, Virginia Vassilevska, Wein, Nicole, Dalirrooyfard, Mina, Vyas, Nikhil, Xu, Yinzhan et al. 2019. "Approximation algorithms for min-distance problems." Leibniz International Proceedings in Informatics, LIPIcs, 132.
Version
Final published version
Abstract
© Graham Cormode, Jacques Dark, and Christian Konrad; licensed under Creative Commons License CC-BY We study fundamental graph parameters such as the Diameter and Radius in directed graphs, when distances are measured using a somewhat unorthodox but natural measure: the distance between u and v is the minimum of the shortest path distances from u to v and from v to u. The center node in a graph under this measure can for instance represent the optimal location for a hospital to ensure the fastest medical care for everyone, as one can either go to the hospital, or a doctor can be sent to help. By computing All-Pairs Shortest Paths, all pairwise distances and thus the parameters we study can be computed exactly in Õ(mn) time for directed graphs on n vertices, m edges and nonnegative edge weights. Furthermore, this time bound is tight under the Strong Exponential Time Hypothesis [Roditty-Vassilevska W. STOC 2013] so it is natural to study how well these parameters can be approximated in O(mn1−ε) time for constant ε > 0. Abboud, Vassilevska Williams, and Wang [SODA 2016] gave a polynomial factor approximation for Diameter and Radius, as well as a constant factor approximation for both problems in the special case where the graph is a DAG. We greatly improve upon these bounds by providing the first constant factor approximations for Diameter, Radius and the related Eccentricities problem in general graphs. Additionally, we provide a hierarchy of algorithms for Diameter that gives a time/accuracy trade-off.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
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Creative Commons Attribution 4.0 International license
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DOI of Published Version
https://doi.org/10.4230/LIPIcs.ICALP.2019.46
