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Eccentricity queries and beyond using Hub Labels
[article]

2020
*
arXiv
*
pre-print

Finally, as

arXiv:2010.15794v1
fatcat:wmryi7mnabfehkfe4cutqifhdu
*a*by-product*of*our approach, on any fixed class*of*unweighted*graphs*with*bounded*expansion, we can decide whether the diameter*of*an n-vertex*graph*in the class is at most k in f(k) · n^*1*... Indeed, given*a*hub labeling*of*maximum label size ≤ k, after pre-processing the labels in total 2^O(k)· |V|^*1*+o(*1*) time, we can compute both the eccentricity and the distance-sum*of*any vertex in 2^O( ... For instance, it was conjectured in [3] that all*graphs**of**highway**dimension*at most h admit*a*hub labeling with maximum label size O(h). ...##
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An Indexing Framework for Queries on Probabilistic Graphs

2017
*
ACM Transactions on Database Systems
*

In

doi:10.1145/3044713
fatcat:4ekoy7ahwbamhojmvse62yfafy
*a**graph*that depicts the relationship*of*authors*of*Wikipedia entries, the existence*of*edges may not be de nite. ... To tackle these issues, we study the ProbTree,*a*data structure that stores*a*succinct, or indexed, version*of*the possible worlds*of*the*graph*. ... ACKNOWLEDGMENTS Reynold Cheng and Silviu Maniu were supported by the Research Grants Council*of*HK (Project HKU 17205115 and 17229116) and HKU (Projects 102009508 and 104004129) . ...##
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Structural Parameters, Tight Bounds, and Approximation for (k,r)-Center
[article]

2018
*
arXiv
*
pre-print

Specifically: - For any r>

arXiv:1704.08868v4
fatcat:gulg3bjn2jakdayx7atmiru6ky
*1*, we show an algorithm that solves the problem in O^*((3r+*1*)^cw) time, where cw is the clique-width*of*the input*graph*, as well as*a*tight SETH lower*bound*matching this algorithm's ... In this paper we provide*a*number*of*tight fine-grained*bounds*on the complexity*of*this problem with respect to various standard*graph*parameters. ... Acknowledgement The very useful remarks and suggestions*of*the two anonymous referees are gratefully acknowledged. ...##
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Wayfinding in Social Networks
[chapter]

2010
*
Computer Communications and Networks
*

In this chapter, I will highlight

doi:10.1007/978-1-84882-765-3_18
dblp:series/ccn/Liben-Nowell10
fatcat:ji5i62e3x5cbdcfwsjfl7n3ipu
*a*recent line*of*computational research*into*the modeling and analysis*of*the small-world phenomenon-the observation that typical pairs*of*people in*a*social network are ... connected by very short chains*of*intermediate friends-and the ability*of*members*of**a*large social network to collectively find efficient routes to reach individuals in the network. ... These papers then typically state*bounds*on navigability that are based on certain structural parameters*of*the underlying*graph*; examples include networks that have*low**treewidth*[16] ,*bounded*growth ...##
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Approximation algorithms for regret minimization in vehicle routing problems

2014

The

doi:10.5075/epfl-thesis-6163
fatcat:c6oyfn2grzh7jge3on2rk3giaq
*treewidth**of*G is the minimum width*of**a*tree decomposition*of*G. We say the*treewidth**of**a*family*of**graphs*is*bounded*if it is O(*1*). ... Solving OP on*graphs*with*bounded**treewidth*is only*a*preliminary step towards*a*potential PTAS for OP on planar*graphs*. ... This fact follows simply from step 4*of*the greedy algorithm, where we distribute*a*value*of**1*among the newly covered nodes. (ii) We can upper*bound*the price*of*any node v as follows. ...