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AORM: Fast Incremental Arbitrary-Order Reachability Matrix Computation for Massive Graphs

Sung-Soo Kim, Young-Kuk Kim, Young-Min Kang
2021 IEEE Access  
In particular, the proposed method outperforms up to 10 times compared to NetworkX for incremental allpairs shortest paths computation.  ...  We focus on the arbitrary-order reachability matrix framework called AORM, which can handle directed and disconnected networks such as citation networks.  ...  In contrast, we present a novel incremental reachability matrix computation approach without any matrix multiplications.  ... 
doi:10.1109/access.2021.3077888 fatcat:dw6qm3xb65fsrpgqrh4uomoipi

Page 47 of Mathematical Reviews Vol. , Issue 2000a [page]

2000 Mathematical Reviews  
estimation of diameter and shortest paths (without matrix multiplication).  ...  Unfortunately, all the new algorithms are based on fast matrix multiplication algorithms that are notori- ously impractical.  ... 

Finding maximally disconnected subnetworks with shortest path tractography

Clint Greene, Matt Cieslak, Lukas J. Volz, Lukas Hensel, Christian Grefkes, Ken Rose, Scott T. Grafton
2019 NeuroImage: Clinical  
The methods provide a fast, reliable approach for both visualizing and quantifying the disconnected portion of a patient's structural connectome based on their routine clinical MRI, without reliance on  ...  Percent connectivity loss matrices are constructed by measuring the proportion of shortest-path probability weighted connections that are lost because of an intersection with the patient's lesion.  ...  Acknowledgements Supported by a grant from the General Electric-National Football League Head Health Challenge and the Institute for Collaborative Biotechnologies through grant W911NF-09-0001 from the  ... 
doi:10.1016/j.nicl.2019.101903 pmid:31491834 pmcid:PMC6627647 fatcat:tmhxck6qzrd6fjw7cugwi3ta7u

Space-Efficient Fault-Tolerant Diameter Oracles [article]

Davide Bilò, Sarel Cohen, Tobias Friedrich, Martin Schirneck
2021 arXiv   pre-print
With fast matrix multiplication, we achieve a preprocessing time of O(n^2.5794 + n^2/ε).  ...  When using fast matrix multiplication instead, the preprocessing time can be improved to n^ω+o(1), where ω < 2.373 is the matrix multiplication exponent.  ...  Algebraic algorithms are known to improve the preprocessing times, if one is willing to employ fast matrix multiplication (for e.g., see [28, 12] and the references therein). Diameter computation.  ... 
arXiv:2107.03485v1 fatcat:3a2l7rvbifdyzjiu4q23fhf7uu

Approximating Cycles in Directed Graphs: Fast Algorithms for Girth and Roundtrip Spanners [article]

Jakub Pachocki, Liam Roditty, Aaron Sidford, Roei Tov, Virginia Vassilevska Williams
2018 arXiv   pre-print
We show that the runtime of our algorithm cannot be significantly improved without a breakthrough in combinatorial Boolean matrix multiplication.  ...  The girth of a graph, i.e. the length of its shortest cycle, is a fundamental graph parameter.  ...  We use our roundtrip cover algorithm to compute multiplicative roundtrip spanners and obtain multiplicative estimates of the girth.  ... 
arXiv:1611.00721v2 fatcat:buf4rgd3rjedvo67nci2hdypk4

Algorithms of Fast Search of Center, Radius and Diameter on Weighted Graphs [article]

Airat Urakov, Timofey Timeryaev
2012 arXiv   pre-print
The radius, diameter and at least one center and one pair of peripheral vertices of the graph are to be found. In the second problem we have additionally calculated the distances matrix.  ...  For the problems being considered, we proposed fast search algorithms which use only small fraction of graph's vertices for the search of the metric characteristics.  ...  A matrix consisting of the shortest paths between all pairs of vertices of a graph is called the distance matrix and is denoted by M = (m ij ).  ... 
arXiv:1209.4761v1 fatcat:4ictevbygjhnlk5eazuap2oeeq

Fast approximate shortest paths in the congested clique

Keren Censor-Hillel, Michal Dory, Janne H. Korhonen, Dean Leitersdorf
2020 Distributed computing  
Our main techniques are new distance tools that are obtained via improved algorithms for sparse matrix multiplication, which we leverage to construct efficient hopsets and shortest paths.  ...  Furthermore, our techniques extend to additional distance problems for which we improve upon the state-of-the-art, including diameter approximation, and an exact single-source shortest paths algorithm  ...  Acknowledgements Open access funding provided by Institute of Science and Technology (IST Austria). We thank Mohsen Ghaffari, Michael Elkin and Merav Parter for fruitful discussions.  ... 
doi:10.1007/s00446-020-00380-5 fatcat:t3qh3oh655cvvkpmdyuq3n3wda

Indexing Network Structure with Shortest-Path Trees

Marc Maier, Matthew Rattigan, David Jensen
2011 ACM Transactions on Knowledge Discovery from Data  
Short paths can be found efficiently by utilizing an index of network structure, which estimates network distances and enables rapid discovery of short paths.  ...  We present results on real data sets for several applications, including navigation, diameter estimation, centrality computation, and clustering-all made efficient by virtue of the network structure index  ...  ACKNOWLEDGMENTS The authors wish to thank Cindy Loiselle for her helpful comments and Kevin Fall for recommending stretch as a measure of routing performance.  ... 
doi:10.1145/1993077.1993079 fatcat:hh6dbwhf2rfrlbxuqmbyeazwpq

Fast approximation algorithms for the diameter and radius of sparse graphs

Liam Roditty, Virginia Vassilevska Williams
2013 Proceedings of the 45th annual ACM symposium on Symposium on theory of computing - STOC '13  
The fastest combinatorial algorithm for both parameters works by solving the all-pairs shortest paths problem (APSP) and has a running time of O(mn) in m-edge, n-node graphs.  ...  In a seminal paper, Aingworth, Chekuri, Indyk and Motwani [SODA'96 and SICOMP'99] presented an algorithm that computes in O(m √ n + n 2 ) time an estimateD for the diameter D, such that ⌊2/3D⌋ ≤D ≤ D.  ...  The second author wants to thank Bob Tarjan for asking whether there is an almost linear time approximation scheme for the diameter, and Ryan Williams for many discussions on the hardness of diameter and  ... 
doi:10.1145/2488608.2488673 dblp:conf/stoc/RodittyW13 fatcat:ljgimx22qvg77phq237fn7m4ai

Suitability Analysis of Routing Algorithms for Web-based Transportation Planning

Davis Jaunzems, Arnis Lektauers
2013 Information Technology and Management Science  
The objectives of the presented research are to examine existing routing algorithms used for finding the shortest path between the nodes in transport networks and to analyse the implementation possibilities  ...  and efficiency of routing algorithms in web-based geographical information systems.  ...  Fig. 1 . 1 Latvia's road and city map Fig. 2 . 2 Graph diameter range across multiple densities Fig. 3 . 3 Computation times required for the search of all the shortest paths 82 Fig. 4 . 4 Computation  ... 
doi:10.2478/itms-2013-0012 fatcat:rhj4nyaemfekjhciad4ddyh6ye

Shortest triplet clustering: reconstructing large phylogenies using representative sets

Le Sy Vinh, Arndt von Haeseler
2005 BMC Bioinformatics  
Based on k-representative sets, shortest triplets are reconstructed and serve as building blocks for the STC algorithm to agglomerate sequences for tree reconstruction in O(n2) time for n sequences.  ...  The main idea is the introduction of a natural definition of so-called k-representative sets.  ...  We thank Gunter Weiss, Ingo Ebersberger, Tanja Gesell and Jutta Buschbom for carefully reading the manuscript.  ... 
doi:10.1186/1471-2105-6-92 pmid:15819989 pmcid:PMC1097715 fatcat:7ohey7jjxrglvcy4we75fbmuhy

Approximating the diameter of a graph [article]

Liam Roditty, Virginia Vassilevska Williams
2012 arXiv   pre-print
In this paper we consider the fundamental problem of approximating the diameter $D$ of directed or undirected graphs. In a seminal paper, Aingworth, Chekuri, Indyk and Motwani [SIAM J.  ...  Comput. 1999] presented an algorithm that computes in $\Ot(m\sqrt n + n^2)$ time an estimate $\hat{D}$ for the diameter of an $n$-node, $m$-edge graph, such that $\lfloor 2/3 D \rfloor \leq \hat{D} \leq  ...  Acknowledgements The first author wants to thank Edith Cohen, Haim Kaplan and Yahav Nussbaum for fruitful discussions on the problem.  ... 
arXiv:1207.3622v1 fatcat:7tdkk4lfovdb3df5tzcc6yphtq

Fast Diameter Computation of Large Sparse Graphs Using GPUs

Giso H. Dal, Walter A. Kosters, Frank W. Takes
2014 2014 22nd Euromicro International Conference on Parallel, Distributed, and Network-Based Processing  
The diameter is defined as the length of the longest shortest path between vertices in the graph, and serves as a relevant property of all types of graphs that are nowadays frequently studied.  ...  We furthermore include a comparison of different GPU algorithms for single-source shortest path computations, which is not only a crucial step in computing the diameter, but also relevant in many other  ...  Most methods break up the APSP into multiple Single-Source Shortest Path (SSSP) problems and then compute the length of these paths in parallel.  ... 
doi:10.1109/pdp.2014.17 dblp:conf/pdp/DalKT14 fatcat:bvufcho4uvejhhntri2okvarym

Conditional Hardness for Sensitivity Problems

Monika Henzinger, Andrea Lincoln, Stefan Neumann, Virginia Vassilevska Williams, Marc Herbstritt
2017 Innovations in Theoretical Computer Science  
For example, we show that under the Boolean Matrix Multiplication (BMM) conjecture combinatorial algorithms cannot compute the (4/3 − ε)-approximate diameter of an undirected unweighted dense graph with  ...  We extend our reduction from BMM to Diameter to give a reduction from All Pairs Shortest Paths to Diameter under one deletion in weighted graphs.  ...  Powers of tensors and fast matrix multiplication. In ISSAC, pages 296-303, 2014. 26 Fabrizio Grandoni and Virginia Vassilevska Williams.  ... 
doi:10.4230/lipics.itcs.2017.26 dblp:conf/innovations/HenzingerL0W17 fatcat:6mw52rwkafcothehbz4nua27wq

Optimal distributed all pairs shortest paths and applications

Stephan Holzer, Roger Wattenhofer
2012 Proceedings of the 2012 ACM symposium on Principles of distributed computing - PODC '12  
On the positive side, we provide an algorithm that achieves such a speedup of D and computes an 1 + ε multiplicative approximation of the diameter.  ...  We present an algorithm to compute All Pairs Shortest Paths (APSP) of a network in a distributed way.  ...  (or performing matrix multiplication.)  ... 
doi:10.1145/2332432.2332504 dblp:conf/podc/HolzerW12 fatcat:dq3k4wwuq5cbtdzl7qedacxieq
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