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Computing the Eccentricity Distribution of Large Graphs

Frank Takes, Walter Kosters
2013 Algorithms  
distribution 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.  ... 
doi:10.3390/a6010100 fatcat:lcz55esjp5cnbidqxfpvst75ym

Estimating the Percolation Centrality of Large Networks through Pseudo-dimension Theory [article]

Alane M. de Lima, Murilo V. G. da Silva, André L. Vignatti
2020 arXiv   pre-print
The estimation obtained by the 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  ... 
arXiv:1910.00494v3 fatcat:awioz33xqbcljgayiwbsugopv4

Real-Time Diameter Monitoring for Time-Evolving Graphs [chapter]

Yasuhiro Fujiwara, Makoto Onizuka, Masaru Kitsuregawa
2011 Lecture Notes in Computer Science  
Our theoretical analyses show that G-Scale guarantees 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.  ... 
doi:10.1007/978-3-642-20149-3_24 fatcat:iejyscxl4bhitp5pvb5noxzyx4

On Computing the Diameter of Real-World Directed (Weighted) Graphs [chapter]

Pierluigi Crescenzi, Roberto Grossi, Leonardo Lanzi, Andrea Marino
2012 Lecture Notes in Computer Science  
In this paper we propose a new 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.  ... 
doi:10.1007/978-3-642-30850-5_10 fatcat:iyagvapjgnfi5mbu6qtjfmaelm

Computing Top-k Closeness Centrality Faster in Unweighted Graphs

Elisabetta Bergamini, Michele Borassi, Pierluigi Crescenzi, Andrea Marino, Henning Meyerhenke
2015 2016 Proceedings of the Eighteenth Workshop on Algorithm Engineering and Experiments (ALENEX)  
Combining them yields 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.  ... 
doi:10.1137/1.9781611974317.6 dblp:conf/alenex/BergaminiBCMM16 fatcat:jys7xwyckfas3m7nrflm6toe6i

Determining the diameter of small world networks

Frank W. Takes, Walter A. Kosters
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 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  ... 
doi:10.1145/2063576.2063748 dblp:conf/cikm/TakesK11 fatcat:desrvsasp5az7okivkalr3lgoq

Dynamic Approximate Shortest Paths and Beyond: Subquadratic and Worst-Case Update Time [article]

Jan van den Brand, Danupon Nanongkai
2019 arXiv   pre-print
Our 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.  ... 
arXiv:1909.10850v2 fatcat:xecognte6jbupk2r6slt4za25u

Big graph mining

U. Kang, Christos Faloutsos
2013 SIGKDD Explorations  
We introduce GIM-V, 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.  ... 
doi:10.1145/2481244.2481249 fatcat:fzidqzmctndj3nxh2qw55txyuu

An Evaluation of Parallel Eccentricity Estimation Algorithms on Undirected Real-World Graphs

Julian Shun
2015 Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD '15  
Our experiments on 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  ... 
doi:10.1145/2783258.2783333 dblp:conf/kdd/Shun15 fatcat:57idyj7otvcsbgds6xshfanjvm

On the Solvability of the Six Degrees of Kevin Bacon Game [chapter]

Michele Borassi, Pierluigi Crescenzi, Michel Habib, Walter Kosters, Andrea Marino, Frank Takes
2014 Lecture Notes in Computer Science  
In this paper, we will propose a new 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.  ... 
doi:10.1007/978-3-319-07890-8_5 fatcat:u4urppl77fhi5gnoxxnnorqrw4

HADI

U. Kang, Charalampos E. Tsourakakis, Ana Paula Appel, Christos Faloutsos, Jure Leskovec
2011 ACM Transactions on Knowledge Discovery from Data  
There are two major contributions in this article: (a) We propose HADI (HAdoop 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.  ... 
doi:10.1145/1921632.1921634 fatcat:lari6gn7p5gpbeag4lfl6a4kxm

Approximating Betweenness Centrality in Fully Dynamic Networks

Elisabetta Bergamini, Henning Meyerhenke
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.  ... 
doi:10.1080/15427951.2016.1177802 fatcat:gr6zvp4bkbd25jbl2spg4tyzaq

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

Clémence Magnien, Matthieu Latapy, Michel Habib
2009 ACM Journal of Experimental Algorithmics  
The 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.  ... 
doi:10.1145/1412228.1455266 fatcat:sy3btt6vk5emtgx4upirs5tyjy

Fast centrality approximation in modular networks

Shu Yan Chan, Ian X.Y. Leung, Pietro Liò
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.  ... 
doi:10.1145/1651274.1651282 dblp:conf/cikm/ChanLL09 fatcat:6bllqdqhazha7mx7ichmppgvl4

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 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.  ... 
doi:10.35940/ijrte.d4273.118419 fatcat:giqwgxgqubhsbclnlmsmvksznq
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