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Computing the Eccentricity Distribution of Large Graphs

2013
*
Algorithms
*

distribution

doi:10.3390/a6010100
fatcat:lcz55esjp5cnbidqxfpvst75ym
*of*various*large**real*-world*graphs*. ... We perform*an*extensive set*of*experiments on a number*of**large**graphs*in order to measure and compare the performance*of*our*algorithms*, and demonstrate how we can efficiently compute the eccentricity ... This research is part*of*the COMPASS project, financed by NWO under grant number 612.065.926. ...##
###
Estimating the Percolation Centrality of Large Networks through Pseudo-dimension Theory
[article]

2020
*
arXiv
*
pre-print

The estimation obtained by the

arXiv:1910.00494v3
fatcat:awioz33xqbcljgayiwbsugopv4
*algorithm*is within ϵ*of*the*exact*value with probability 1-δ,*for*fixed constants 0 < ϵ,δ≤ 1. ... In fact, we show in our experimental analysis that in the case*of**real*world complex networks, the output produced by our*algorithm*is significantly closer to the*exact*values than its guarantee in terms ... Table 1: Datasets details*for*the*real*-world*graphs*.*exact*time approx. time*Graph*Type |V | |E| V D(G) Min Max wiki-Vote*Directed*7115 103689 11 10.21 10.49 p2p-Gnutella08*Directed*6301 ...##
###
Real-Time Diameter Monitoring for Time-Evolving Graphs
[chapter]

2011
*
Lecture Notes in Computer Science
*

Our theoretical analyses show that G-Scale guarantees

doi:10.1007/978-3-642-20149-3_24
fatcat:iejyscxl4bhitp5pvb5noxzyx4
*exactness*in identifying the*diameter*. We perform several experiments on*real*and*large*datasets. ... The goal*of*this work is to identify the*diameter*, the maximum distance between any two nodes,*of**graphs*that evolve over time. ... In other words, the goal*of*this work is continuous*diameter*monitoring*for*time-evolving*graphs*. We propose*an**algorithm*to solve this problem exactly in*real*-time. ...##
###
On Computing the Diameter of Real-World Directed (Weighted) Graphs
[chapter]

2012
*
Lecture Notes in Computer Science
*

In this paper we propose a new

doi:10.1007/978-3-642-30850-5_10
fatcat:iyagvapjgnfi5mbu6qtjfmaelm
*algorithm**for*computing the*diameter**of**directed*unweighted*graphs*. ... Moreover, we show how to extend our*algorithm*to the case*of**directed*weighted*graphs*and, even in this case, we present some preliminary very positive experimental results. ... As far as we know, difub is the first*algorithm*which is able to compute exactly the*diameter**of*the strongly connected components*of*huge*real*-world*directed**graphs*. ...##
###
Computing Top-k Closeness Centrality Faster in Unweighted Graphs

2015
*
2016 Proceedings of the Eighteenth Workshop on Algorithm Engineering and Experiments (ALENEX)
*

Combining them yields

doi:10.1137/1.9781611974317.6
dblp:conf/alenex/BergaminiBCMM16
fatcat:jys7xwyckfas3m7nrflm6toe6i
*an**algorithm*that is faster than the state*of*the art*for*top-k computations*for*all test instances, by a wide margin*for*high-*diameter** E. B.'s and H. M.' ... Thus, even*for*sparse*graphs*, these*algorithms*require quadratic running time in the worst case, which is prohibitive*for**large*networks. ... We would like to thank Moritz von Looz*for*providing the hyperbolic random*graphs*used in our experiments and numerous contributors to the NetworKit project. ...##
###
Determining the diameter of small world networks

2011
*
Proceedings of the 20th ACM international conference on Information and knowledge management - CIKM '11
*

In this paper we present a novel approach to determine the

doi:10.1145/2063576.2063748
dblp:conf/cikm/TakesK11
fatcat:desrvsasp5az7okivkalr3lgoq
*exact**diameter*(longest shortest path length)*of**large**graphs*, in particular*of*the nowadays frequently studied small world networks. ... We will show that our*algorithm*is able to quickly determine the*exact**diameter**of*various*large*datasets*of*small world networks with millions*of*nodes and hundreds*of*millions*of*links, whereas before ...*Exact**algorithms**for*calculating this*diameter*traditionally require running*an*All Pairs Shortest Path (APSP)*algorithm**for*each node in the network, ultimately returning the length*of*one*of*the longest ...##
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Dynamic Approximate Shortest Paths and Beyond: Subquadratic and Worst-Case Update Time
[article]

2019
*
arXiv
*
pre-print

Our

arXiv:1909.10850v2
fatcat:xecognte6jbupk2r6slt4za25u
*algorithm*with I={s} and J=V(G) implies a (1+ϵ)-approximation*algorithm**for*this, guaranteeing Õ(n^1.823/ϵ^2) worst-case update time*for**directed**graphs*with positive*real*weights in [1, W]. ... Consider the following distance query*for**an*n-node*graph*G undergoing edge insertions and deletions: given two sets*of*nodes I and J, return the distances between every pair*of*nodes in I× J. ... We run a modification*of*Corollary 4.7. We first explain how to obtain the*diameter*, then we explain how to modify the*algorithm*to obtain a faster update complexity. ...##
###
Big graph mining

2013
*
SIGKDD Explorations
*

We introduce GIM-V,

doi:10.1145/2481244.2481249
fatcat:fzidqzmctndj3nxh2qw55txyuu
*an*important primitive that Pegasus uses*for*its*algorithms*to analyze structures*of**large**graphs*. ... Using Pegasus, we analyze very*large*,*real*world*graphs*with billions*of*nodes and edges. ... The views and conclusions are those*of*the authors and should not be interpreted as representing the official policies,*of*the U.S. ...##
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An Evaluation of Parallel Eccentricity Estimation Algorithms on Undirected Real-World Graphs

2015
*
Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD '15
*

Our experiments on

doi:10.1145/2783258.2783333
dblp:conf/kdd/Shun15
fatcat:57idyj7otvcsbgds6xshfanjvm
*large*undirected*real*-world*graphs*show that the*algorithm*based on two-pass breadth-first searches works surprisingly well, outperforming the other*algorithms*in terms*of*running time ... The high accuracy, efficiency, and parallelism*of*our best implementation allows the fast generation*of*eccentricity estimates*for**large**graphs*, which are useful in many applications arising in*large*-scale ... This work is partially supported by the National Science Foundation under grant CCF-1314590, and by the Intel Labs Academic Research Office*for*the Parallel*Algorithms*...##
###
On the Solvability of the Six Degrees of Kevin Bacon Game
[chapter]

2014
*
Lecture Notes in Computer Science
*

In this paper, we will propose a new

doi:10.1007/978-3-319-07890-8_5
fatcat:u4urppl77fhi5gnoxxnnorqrw4
*algorithm*that computes the radius and the*diameter**of*a*graph*G = (V, E), by finding bounds through heuristics and improving them until*exact*values can be guaranteed ... As*an*application example, we use our new*algorithm*in order to determine the solvability over time*of*the "six degrees*of*Kevin Bacon" game. ... Conclusion In this paper, we proposed a new heuristic to upper and lower bound respectively the radius and*diameter**of**large**graphs*and a new*algorithm**for*computing their*exact*value. ...
There are two major contributions in this article: (a) We propose HADI (HAdoop

doi:10.1145/1921632.1921634
fatcat:lari6gn7p5gpbeag4lfl6a4kxm
*DIameter*and radii estimator), a carefully designed and fine-tuned*algorithm*to compute the radii and the*diameter**of*massive ... In this article we define the Radius plot*of*a*graph*and show how it can answer these questions. However, computing the Radius plot is prohibitively expensive*for**graphs*reaching the planetary scale. ...*for*the web*graph*and access to the M45, and Adriano A. Paterlini*for*feedback. The opinions expressed are those*of*the authors and do not necessarily reflect the views*of*the funding agencies. ...##
###
Approximating Betweenness Centrality in Fully Dynamic Networks

2016
*
Internet Mathematics
*

*of*the vertex

*diameter*in undirected

*graphs*, and (iii)

*an*

*algorithm*with lower time complexity

*for*updating single-source shortest paths in unweighted

*graphs*after a batch

*of*edge actions. ... Because

*exact*computations are prohibitive in

*large*networks, several approximation

*algorithms*have been proposed. ... We also thank Matteo Riondato

*for*his constructive comments on earlier versions

*of*the material presented in this article. ...

##
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Fast computation of empirically tight bounds for the diameter of massive graphs

2009
*
ACM Journal of Experimental Algorithmics
*

The

doi:10.1145/1412228.1455266
fatcat:sy3btt6vk5emtgx4upirs5tyjy
*diameter**of*a*graph*is among its most basic parameters. Since a few years, it moreover became a key issue to compute it*for*massive*graphs*in the context*of*complex network analysis. ... We propose here a new approach relying on very simple and fast*algorithms*that compute (upper and lower) bounds*for*the*diameter*. ... We thank Vincent Limouzy, as well as the anonymous referees,*for*helpful comments and references. ...##
###
Fast centrality approximation in modular networks

2009
*
Proceeding of the 1st ACM international workshop on Complex networks meet information & knowledge management - CNIKM '09
*

*Exact*inference

*of*centrality values is infeasible in

*large*networks due to the need to solve the all-pairs shortest path problem. ... Measuring the centrality

*of*nodes in

*real*-world networks has remained

*an*important task in the technological, social, and biological network paradigms carrying implications on their analysis and applications ... The

*exact*calculation

*of*the closeness requires solving the APSP problem and hence require O(nm) in

*an*unweighed network which is prohibitive in

*large*networks. ...

##
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Implicit Landmark Path Indexing for Bounded Label Constrained Reachable Paths

2019
*
International journal of recent technology and engineering
*

We extended the LCR queries by considering weighted

doi:10.35940/ijrte.d4273.118419
fatcat:giqwgxgqubhsbclnlmsmvksznq
*directed**graphs*and proposed a novel technique*of*finding paths*for*LCR queries bounded by path weight. ... with*an*additional total path weight constraint, and (2) the need to discover a technique that finds*exact*reachable paths between the given vertices. ... Hence, we index the paths*of*length less than or equal to half the*diameter**of*the*graph**for*the nodes*for*faster indexing to handle*large**graphs*. ...
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