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Eccentricity queries and beyond using Hub Labels [article]

Guillaume Ducoffe
2020 arXiv   pre-print
Finally, as 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).  ... 
arXiv:2010.15794v1 fatcat:wmryi7mnabfehkfe4cutqifhdu

An Indexing Framework for Queries on Probabilistic Graphs

Silviu Maniu, Reynold Cheng, Pierre Senellart
2017 ACM Transactions on Database Systems  
In 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) .  ... 
doi:10.1145/3044713 fatcat:4ekoy7ahwbamhojmvse62yfafy

Structural Parameters, Tight Bounds, and Approximation for (k,r)-Center [article]

Ioannis Katsikarelis, Michael Lampis, Vangelis Th. Paschos
2018 arXiv   pre-print
Specifically: - For any r> 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.  ... 
arXiv:1704.08868v4 fatcat:gulg3bjn2jakdayx7atmiru6ky

Wayfinding in Social Networks [chapter]

David Liben-Nowell
2010 Computer Communications and Networks  
In this chapter, I will highlight 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  ... 
doi:10.1007/978-1-84882-765-3_18 dblp:series/ccn/Liben-Nowell10 fatcat:ji5i62e3x5cbdcfwsjfl7n3ipu

Approximation algorithms for regret minimization in vehicle routing problems

Adrian Aloysius Bock
2014
The 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.  ... 
doi:10.5075/epfl-thesis-6163 fatcat:c6oyfn2grzh7jge3on2rk3giaq