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AORM: Fast Incremental Arbitrary-Order Reachability Matrix Computation for Massive Graphs
2021
IEEE Access
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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
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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
2019
NeuroImage: Clinical
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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]
2021
arXiv
pre-print
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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]
2018
arXiv
pre-print
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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]
2012
arXiv
pre-print
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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
2020
Distributed computing
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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
2011
ACM Transactions on Knowledge Discovery from Data
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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
2013
Proceedings of the 45th annual ACM symposium on Symposium on theory of computing - STOC '13
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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
2013
Information Technology and Management Science
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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
2005
BMC Bioinformatics
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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]
2012
arXiv
pre-print
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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
2014
2014 22nd Euromicro International Conference on Parallel, Distributed, and Network-Based Processing
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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
2017
Innovations in Theoretical Computer Science
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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
2012
Proceedings of the 2012 ACM symposium on Principles of distributed computing - PODC '12
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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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