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

2021
*
IEEE Access
*

In particular, the proposed method outperforms up to 10 times compared to NetworkX for incremental allpairs

doi:10.1109/access.2021.3077888
fatcat:dw6qm3xb65fsrpgqrh4uomoipi
*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*. ...##
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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. ...

##
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Finding maximally disconnected subnetworks with shortest path tractography

2019
*
NeuroImage: Clinical
*

The methods provide a

doi:10.1016/j.nicl.2019.101903
pmid:31491834
pmcid:PMC6627647
fatcat:tmhxck6qzrd6fjw7cugwi3ta7u
*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 ...##
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Space-Efficient Fault-Tolerant Diameter Oracles
[article]

2021
*
arXiv
*
pre-print

With

arXiv:2107.03485v1
fatcat:3a2l7rvbifdyzjiu4q23fhf7uu
*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. ...##
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Approximating Cycles in Directed Graphs: Fast Algorithms for Girth and Roundtrip Spanners
[article]

2018
*
arXiv
*
pre-print

We show that the runtime

arXiv:1611.00721v2
fatcat:buf4rgd3rjedvo67nci2hdypk4
*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. ...##
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Algorithms of Fast Search of Center, Radius and Diameter on Weighted Graphs
[article]

2012
*
arXiv
*
pre-print

The radius,

arXiv:1209.4761v1
fatcat:4ictevbygjhnlk5eazuap2oeeq
*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 ). ...##
###
Fast approximate shortest paths in the congested clique

2020
*
Distributed computing
*

Our main techniques are new distance tools that are obtained via improved algorithms for sparse

doi:10.1007/s00446-020-00380-5
fatcat:t3qh3oh655cvvkpmdyuq3n3wda
*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. ...##
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Indexing Network Structure with Shortest-Path Trees

2011
*
ACM Transactions on Knowledge Discovery from Data
*

Short

doi:10.1145/1993077.1993079
fatcat:hh6dbwhf2rfrlbxuqmbyeazwpq
*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. ...##
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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
*

The fastest combinatorial algorithm for both parameters works by solving the all-pairs

doi:10.1145/2488608.2488673
dblp:conf/stoc/RodittyW13
fatcat:ljgimx22qvg77phq237fn7m4ai
*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*...##
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Suitability Analysis of Routing Algorithms for Web-based Transportation Planning

2013
*
Information Technology and Management Science
*

The objectives

doi:10.2478/itms-2013-0012
fatcat:rhj4nyaemfekjhciad4ddyh6ye
*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 ...##
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Shortest triplet clustering: reconstructing large phylogenies using representative sets

2005
*
BMC Bioinformatics
*

Based on k-representative sets,

doi:10.1186/1471-2105-6-92
pmid:15819989
pmcid:PMC1097715
fatcat:7ohey7jjxrglvcy4we75fbmuhy
*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. ...##
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Approximating the diameter of a graph
[article]

2012
*
arXiv
*
pre-print

In this paper we consider the fundamental problem

arXiv:1207.3622v1
fatcat:7tdkk4lfovdb3df5tzcc6yphtq
*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. ...##
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Fast Diameter Computation of Large Sparse Graphs Using GPUs

2014
*
2014 22nd Euromicro International Conference on Parallel, Distributed, and Network-Based Processing
*

The

doi:10.1109/pdp.2014.17
dblp:conf/pdp/DalKT14
fatcat:bvufcho4uvejhhntri2okvarym
*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. ...##
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Conditional Hardness for Sensitivity Problems

2017
*
Innovations in Theoretical Computer Science
*

For example, we show that under the Boolean

doi:10.4230/lipics.itcs.2017.26
dblp:conf/innovations/HenzingerL0W17
fatcat:6mw52rwkafcothehbz4nua27wq
*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. ...##
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Optimal distributed all pairs shortest paths and applications

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

doi:10.1145/2332432.2332504
dblp:conf/podc/HolzerW12
fatcat:dq3k4wwuq5cbtdzl7qedacxieq
*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*.) ...
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