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

Aaron Bernstein, Danupon Nanongkai
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  ... 
arXiv:1811.03337v2 fatcat:goooidrkabezfeyhq5neq7ui34

Better Approximation of Betweenness Centrality [chapter]

Robert Geisberger, Peter Sanders, Dominik Schultes
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 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.  ... 
doi:10.1137/1.9781611972887.9 dblp:conf/alenex/GeisbergerSS08 fatcat:otsw5qw4sze6dczip5gewgp6pm

Near-Linear Time Construction of Sparse Neighborhood Covers

Baruch Awerbuch, Bonnie Berger, Lenore Cowen, David Peleg
1998 SIAM journal on computing (Print)  
For the 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.  ... 
doi:10.1137/s0097539794271898 fatcat:prxro3p77zcprpq2lr7xakotpu

A Survey of Shortest-Path Algorithms [article]

Amgad Madkour, Walid G. Aref, Faizan Ur Rehman, Mohamed Abdur Rahman, Saleh Basalamah
2017 arXiv   pre-print
There is no one general algorithm that is capable of solving 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.  ... 
arXiv:1705.02044v1 fatcat:fkh55mi34vezhbvjbzu7ekmdai

Quality of Service Routing [chapter]

P. Van Mieghem, F. A. Kuipers, T. Korkmaz, M. Krunz, M. Curado, E. Monteiro, X. Masip-Bruin, J. Solé-Pareta, S. Sánchez-López
2003 Lecture Notes in Computer Science  
The expected impact of such an efficient constraint-based routing algorithm has resulted 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  ... 
doi:10.1007/978-3-540-45190-7_3 fatcat:ovefntlsxzgsblapfpsgy6eqqq

Quality-of-Service Routing [chapter]

2017 Network Routing  
The expected impact of such an efficient constraint-based routing algorithm has resulted 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  ... 
doi:10.1002/9781119114864.ch4 fatcat:dqz5ireoprbk5cey4lk2qvfpg4

An Experimental Study of a Parallel Shortest Path Algorithm for Solving Large-Scale Graph Instances [chapter]

Kamesh Madduri, David A. Bader, Jonathan W. Berry, Joseph R. Crobak
2007 2007 Proceedings of the Ninth Workshop on Algorithm Engineering and Experiments (ALENEX)  
We present an experimental study of the single source 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  ... 
doi:10.1137/1.9781611972870.3 dblp:conf/alenex/MadduriBBC07 fatcat:vzlqjuezajaprdd6p7tc52irfe

Performance evaluation of constraint-based path selection algorithms

F. Kuipers, T. Korkmaz, M. Krunz, P. Van Mieghem
2004 IEEE Network  
Numerous heuristics and a few 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.  ... 
doi:10.1109/mnet.2004.1337731 fatcat:iphypnplyfd2vp5ilgmknpdmxi

New Hardness Results for Planar Graph Problems in P and an Algorithm for Sparsest Cut [article]

Amir Abboud and Vincent Cohen-Addad and Philip N. Klein
2020 arXiv   pre-print
For planar inputs the problem is 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 .  ... 
arXiv:2007.02377v1 fatcat:6l6bbpsfxzcb3eacdxdz2xbqwu

Brief Announcement: (1+ε)-Approximate Shortest Paths in Dynamic Streams

Michael Elkin, Chhaya Trehan
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 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  ... 
doi:10.1145/3519270.3538469 fatcat:ahuglaqxd5ek5jskngvyklnl3a

Computing the Greedy Spanner in Near-Quadratic Time

Prosenjit Bose, Paz Carmi, Mohammad Farshi, Anil Maheshwari, Michiel Smid
2009 Algorithmica  
Then, process the 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.  ... 
doi:10.1007/s00453-009-9293-4 fatcat:2x4a3hxsr5dhngm5p7uv3gth7q

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

Atilla Soner Balkir, Huseyin Oktay, Ian Foster
2014 Concurrency and Computation  
Given'as the source (landmark), the traditional definition of this problem asks for finding the 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.  ... 
doi:10.1002/cpe.3354 fatcat:boqyj6pnibeb5frkqgc5sizqay

A distributed approach for multi-constrained path selection and routing optimization

Zhenjiang Li, J. J. Garcia-Luna-Aceves
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 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.  ... 
doi:10.1145/1185373.1185420 dblp:conf/qshine/LiG06 fatcat:wemj7mot2feszlzl77og3jvefa

Lagrangian Relaxation for the Multiple Constrained Robust Shortest Path Problem

Yiyong Pan
2019 Mathematical Problems in Engineering  
The study focuses on a multiple constrained reliable 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.  ... 
doi:10.1155/2019/3987278 fatcat:iz4yjehrn5e2jhxdhr7fi6tl5i
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