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Distributed Exact Weighted All-Pairs Shortest Paths in Near-Linear Time
[article]

2019
*
arXiv
*
pre-print

*In*the

*distributed*

*all*-

*pairs*

*shortest*

*paths*problem (APSP), every node

*in*the

*weighted*undirected

*distributed*network (the CONGEST model) needs to know the distance from every other node using least number ... It was shown that any super-

*linear*lower bound (

*in*n) requires a new technique [Censor-Hillel, Khoury, Paz, DISC'17], but otherwise it remained widely open whether there exists a Õ(n)-

*time*algorithm for ... Abstract

*In*the

*distributed*

*all*-

*pairs*

*shortest*

*paths*problem (APSP), every node

*in*the

*weighted*undirected

*distributed*network (the CONGEST model) needs to know the distance from every other node using ...

##
###
Better Approximation of Betweenness Centrality
[chapter]

2008
*
2008 Proceedings of the Tenth Workshop on Algorithm Engineering and Experiments (ALENEX)
*

Betweenness is one of the most important centrality indices, which basically counts the number of

doi:10.1137/1.9781611972887.9
dblp:conf/alenex/GeisbergerSS08
fatcat:otsw5qw4sze6dczip5gewgp6pm
*shortest**paths*going through a node. ... Betweenness has been used*in*diverse applications, e.g., social network analysis or route planning. Since*exact*computation is prohibitive for large networks, approximation algorithms are important. ... This graph has 392 400 nodes, 16 557 451 edges, and many*shortest**paths*between most*pairs*of nodes. ...##
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Near-Linear Time Construction of Sparse Neighborhood Covers

1998
*
SIAM journal on computing (Print)
*

For the

doi:10.1137/s0097539794271898
fatcat:prxro3p77zcprpq2lr7xakotpu
*all*-*pairs**shortest*... Approximating k-*pairs**shortest**paths*. The k-*pairs**shortest**paths*problem, as discussed*in*the sequel, is defined as follows. ... Subsequently, this result has been further improved*in*[4] , solving*exact**all*-*pairs**shortest**paths**in*the case of integer edge*weights*between 0 and W*in*O(W 2 M (n) log n)*time*. ...##
###
A Survey of Shortest-Path Algorithms
[article]

2017
*
arXiv
*
pre-print

There is no one general algorithm that is capable of solving

arXiv:1705.02044v1
fatcat:fkh55mi34vezhbvjbzu7ekmdai
*all*variants of the*shortest*-*path*problem due to the space and*time*complexities associated with each algorithm. ... A*shortest*-*path*algorithm finds a*path*containing the minimal cost between two vertices*in*a graph. ... Aref's research has been supported*in*part by the National Science Foundation under Grant IIS 1117766. ...##
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Quality of Service Routing
[chapter]

2003
*
Lecture Notes in Computer Science
*

The expected impact of such an efficient constraint-based routing algorithm has resulted

doi:10.1007/978-3-540-45190-7_3
fatcat:ovefntlsxzgsblapfpsgy6eqqq
*in*the proposal of numerous heuristics and a few*exact*QoS algorithms. ... Hence, accurate constraint-based routing algorithms with a fast running*time*are scarce, perhaps even non-existent. ...*In*the class of Waxman or random graphs with uniformly*distributed*link*weights*, simulations suggest that the execution*times*of such*exact*algorithms increase almost linearly with the number of nodes ...##
###
Quality-of-Service Routing
[chapter]

2017
*
Network Routing
*

The expected impact of such an efficient constraint-based routing algorithm has resulted

doi:10.1002/9781119114864.ch4
fatcat:dqz5ireoprbk5cey4lk2qvfpg4
*in*the proposal of numerous heuristics and a few*exact*QoS algorithms. ... Hence, accurate constraint-based routing algorithms with a fast running*time*are scarce, perhaps even non-existent. ...*In*the class of Waxman or random graphs with uniformly*distributed*link*weights*, simulations suggest that the execution*times*of such*exact*algorithms increase almost linearly with the number of nodes ...##
###
An Experimental Study of a Parallel Shortest Path Algorithm for Solving Large-Scale Graph Instances
[chapter]

2007
*
2007 Proceedings of the Ninth Workshop on Algorithm Engineering and Experiments (ALENEX)
*

We present an experimental study of the single source

doi:10.1137/1.9781611972870.3
dblp:conf/alenex/MadduriBBC07
fatcat:vzlqjuezajaprdd6p7tc52irfe
*shortest**path*problem with non-negative edge*weights*(NSSP) on large-scale graphs using the ∆-stepping parallel algorithm. ... To our knowledge, these are the first performance results of a*shortest**path*problem on realistic graph instances*in*the order of billions of vertices and edges. ... Acknowledgments This work was supported*in*part by NSF Grants CNS-0614915, CAREER CCF-0611589, ACI-00-93039, NSF DBI-0420513, ITR ACI-00-81404, ITR EIA-01-21377, Biocomplexity DEB-01-20709, ITR EF/BIO ...##
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Performance evaluation of constraint-based path selection algorithms

2004
*
IEEE Network
*

Numerous heuristics and a few

doi:10.1109/mnet.2004.1337731
fatcat:iphypnplyfd2vp5ilgmknpdmxi
*exact*algorithms have been proposed.*In*this article we compare most of these algorithms. ... We focus on restricted*shortest**path*algorithms and multi-constrained*path*algorithms. ... Some algorithms display a*linear*increase*in*the execution*time*.*All*these algorithms have an initialization phase*in*which they execute the Dijkstra algorithm m*times*. ...##
###
New Hardness Results for Planar Graph Problems in P and an Algorithm for Sparsest Cut
[article]

2020
*
arXiv
*
pre-print

For planar inputs the problem is

arXiv:2007.02377v1
fatcat:6l6bbpsfxzcb3eacdxdz2xbqwu
*in*P and can be solved*in*Õ(n^3)*time*if*all*vertex*weights*are 1. ... To complement the lower bound, we provide a constant factor approximation*in**near*-*linear**time*, improving upon the 25-year old result of Rao*in*both*time*and accuracy. ... Therefore*in*order to obtain a*near*-*linear**time*bound for Find , it suffices to prove a*near*-*linear**time*bound for RootedFind . ...##
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Brief Announcement: (1+ε)-Approximate Shortest Paths in Dynamic Streams

2022
*
Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing
*

Currently existing solutions for this problem either build a sparse multiplicative spanner of the input graph and compute

doi:10.1145/3519270.3538469
fatcat:ahuglaqxd5ek5jskngvyklnl3a
*shortest**paths**in*the spanner offline, or compute an*exact*single source BFS tree ... We show that (1 + ϵ )-approximate single-source*shortest**paths*can be computed with Õ (n 1+1/κ ) space using just constantly many passes*in*unweighted graphs, and polylogarithmically many passes*in**weighted*... Most of the algorithms for computing (approximate) distances and*shortest**paths**in*the streaming setting compute a sparse spanner, and then employ it for computing*exact**shortest**paths*and distances*in*...##
###
Computing the Greedy Spanner in Near-Quadratic Time

2009
*
Algorithmica
*

Then, process the

doi:10.1007/s00453-009-9293-4
fatcat:2x4a3hxsr5dhngm5p7uv3gth7q
*pairs**in*sorted order. Processing a*pair*(u, v) entails a*shortest**path*query*in*G between u and v. ... However, even for points*in*d-dimensional Euclidean space, the greedy algorithm has*near*-cubic running*time*. ... If there exists a real number L such that 1/L is polynomial*in*n and β is*near*-*linear**in*n, then the running*time*of Algorithm 3.1 is*near*-quadratic. ...##
###
Page 3869 of Mathematical Reviews Vol. , Issue 84i
[page]

1984
*
Mathematical Reviews
*

We give a

*linear*algorithm for finding maximum flow values between*all**pairs*of nodes*in*the outerplanar network. ... Its running*time*is O( K-c(n,m)), where n is the number of nodes, m is the number of edges*in*a graph, and c(n,m) is the*time*to compute*shortest**paths*from one node to*all*the other nodes. ...##
###
Estimating graph distance and centrality on shared nothing architectures

2014
*
Concurrency and Computation
*

Given'as the source (landmark), the traditional definition of this problem asks for finding the

doi:10.1002/cpe.3354
fatcat:boqyj6pnibeb5frkqgc5sizqay
*shortest**path*.'; v/ for*all*v 2 V . ... Computing the*exact**shortest**paths*between a large number of vertices is a costly operation, and serial algorithms are not practical for billion-scale graphs. ... However,*in*large networks with millions of nodes and billions of edges, computing the*exact**shortest**paths*between*all**pairs*of nodes is not practical. ...##
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A distributed approach for multi-constrained path selection and routing optimization

2006
*
Proceedings of the 3rd international conference on Quality of service in heterogeneous wired/wireless networks - QShine '06
*

routing of data packets, and implements constrained

doi:10.1145/1185373.1185420
dblp:conf/qshine/LiG06
fatcat:wemj7mot2feszlzl77og3jvefa
*path*optimization by*distributively*constructing an ¥ -optimal*path*set (i.e., the*shortest*, the second*shortest*and up to the ¥ th*shortest**path**in*... For constrained*path*optimization, MPOR has high probabilities of finding feasible*paths*that are also optimal or*near*-optimal for the given optimization metric. ... As the baseline, we also implement an*exact*algorithm, which has exponential running*time*, but can give*all*feasible*paths*for a given routing request. ...##
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Lagrangian Relaxation for the Multiple Constrained Robust Shortest Path Problem

2019
*
Mathematical Problems in Engineering
*

The study focuses on a multiple constrained reliable

doi:10.1155/2019/3987278
fatcat:iz4yjehrn5e2jhxdhr7fi6tl5i
*path*problem*in*which travel*time*reliability and resource constraints are collectively considered. ... Numerical studies indicate that the proposed algorithm is efficient*in*terms of obtaining the close-to-optimal solutions within reasonable computational*times*. ... Acknowledgments This study is sponsored*in*part by National Science Foundation of China under grant No. 51508280 and by Startup Foundation of Nanjing Forestry University under grant No. ...
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