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More Algorithms for All-Pairs Shortest Paths in Weighted Graphs

Timothy M. Chan
2010 SIAM journal on computing (Print)  
APSP in real-vertex-weighted graphs, as well as an improved result (near O(n (3+ω)/2 ) = O(n 2.688 ) time) for the all-pairs lightest shortest path problem for small-integer-weighted graphs.  ...  In the first part of the paper, we reexamine the all-pairs shortest paths (APSP) problem and present a new algorithm with running time O(n 3 log 3 log n/ log 2 n), which improves all known algorithms for  ...  We reiterate the main open question: can the general APSP problem be solved in O(n 3−δ ) time for some positive constant δ?  ... 
doi:10.1137/08071990x fatcat:g6nnaexymra7zcqynpdkbhaz6q

More algorithms for all-pairs shortest paths in weighted graphs

Timothy M. Chan
2007 Proceedings of the thirty-ninth annual ACM symposium on Theory of computing - STOC '07  
APSP in real-vertex-weighted graphs, as well as an improved result (near O(n (3+ω)/2 ) = O(n 2.688 ) time) for the all-pairs lightest shortest path problem for small-integer-weighted graphs.  ...  In the first part of the paper, we reexamine the all-pairs shortest paths (APSP) problem and present a new algorithm with running time O(n 3 log 3 log n/ log 2 n), which improves all known algorithms for  ...  We reiterate the main open question: can the general APSP problem be solved in O(n 3−δ ) time for some positive constant δ?  ... 
doi:10.1145/1250790.1250877 dblp:conf/stoc/Chan07 fatcat:hjvgkpode5cp7oarbre6fvynae

Engineering Shortest Path Algorithms [chapter]

Camil Demetrescu, Giuseppe F. Italiano
2004 Lecture Notes in Computer Science  
In this paper, we report on our own experience in studying a fundamental problem on graphs: all pairs shortest paths.  ...  In particular, we discuss the interplay between theory and practice in engineering a simple variant of Dijkstra's shortest path algorithm.  ...  to the first general efficient dynamic algorithms for maintaining the all pairs shortest paths in a graph.  ... 
doi:10.1007/978-3-540-24838-5_14 fatcat:uggagxe7gfcchbumfusicft2jy

Finding the Hidden Path: Time Bounds for All-Pairs Shortest Paths

David R. Karger, Daphne Koller, Steven J. Phillips
1993 SIAM journal on computing (Print)  
We investigate the all-pairs shortest paths problem in weighted graphs.  ...  We present an algorithm| the Hidden Paths Algorithm|that nds these paths in time O(m n + n 2 log n), where m is the number of edges participating in shortest paths.  ...  Acknowledgements We would like to thank Mike Luby and Cathy Mc-Geoch for pointing out references for path lengths in graphs with random edge weights.  ... 
doi:10.1137/0222071 fatcat:wn3ogqqw4vc5bfsgcjeise6lqy

An Improved Algorithm for Finding All Pair Shortest Path

Himanshu Garg, Paramjeet Rawat
2012 International Journal of Computer Applications  
Floyd Warshall's Algorithm is a simple and widely used algorithm to compute shortest path between all pairs of vertices in an edge weighted directed graph.  ...  We present an O(n ) 3 (   ) time algorithm for finding all pair shortest paths.  ...  Viswanathan Iyer, -All-pairs shortest-paths problem for unweighted graphs time algorithm for all pairs shortest paths‖, Manuscript, 2009. [5] Wikipedia.  ... 
doi:10.5120/7539-0492 fatcat:pxguyxviwbbgxndqd35picwahq

Privacy Preservation in Social Network Analysis using Edge Weight Perturbation

Nayan Mattani, J. Sharath Kumar, A. Prabakaran, N. Maheswari
2016 Indian Journal of Science and Technology  
This is achieved by modification of shortest path length in graphs and also maintains the structure of the graph.  ...  The edge weight perturbation algorithm can be improved by combing the algorithm with the preservation techniques for the user nodes.  ...  For 50% targeted pairs, the correlation coefficient for greedy perturbation is 0.6538205 and Weight Perturbation Shortest Path algorithm is 0.7983018.  ... 
doi:10.17485/ijst/2016/v9i37/93810 fatcat:vxtle63abbfofmsmbj5n3mfmf4

On the difficulty of some shortest path problems

John Hershberger, Subhash Suri, Amit Bhosle
2007 ACM Transactions on Algorithms  
This also establishes a similar lower bound for computing the second shortest simple path by any algorithm that uses replacement paths as a subroutine; all known algorithms for the k shortest paths fit  ...  One interesting connection between the two problems mentioned above (k simple shortest paths and replacement paths) is that all the known k shortest paths algorithms, including those for undirected graphs  ...  Then for any pair (x a , z c ), the shortest path joining them is identical to the shortest path in the original graph H.  ... 
doi:10.1145/1219944.1219951 fatcat:ernhz2cdmjhqnim5ht7ubbblme

On the Difficulty of Some Shortest Path Problems [chapter]

John Hershberger, Subhash Suri, Amit Bhosle
2003 Lecture Notes in Computer Science  
This also establishes a similar lower bound for computing the second shortest simple path by any algorithm that uses replacement paths as a subroutine; all known algorithms for the k shortest paths fit  ...  One interesting connection between the two problems mentioned above (k simple shortest paths and replacement paths) is that all the known k shortest paths algorithms, including those for undirected graphs  ...  Then for any pair (x a , z c ), the shortest path joining them is identical to the shortest path in the original graph H.  ... 
doi:10.1007/3-540-36494-3_31 fatcat:tceizql3cfeadfwcb6aiftuolu

On the difficulty of some shortest path problems

John Hershberger, Subhash Suri, Amit Bhosle
2007 ACM Transactions on Algorithms  
This also establishes a similar lower bound for computing the second shortest simple path by any algorithm that uses replacement paths as a subroutine; all known algorithms for the k shortest paths fit  ...  One interesting connection between the two problems mentioned above (k simple shortest paths and replacement paths) is that all the known k shortest paths algorithms, including those for undirected graphs  ...  Then for any pair (x a , z c ), the shortest path joining them is identical to the shortest path in the original graph H.  ... 
doi:10.1145/1186810.1186815 fatcat:4msbqoswtzhk7nv7qdbhkntkfu

Efficient Network Analysis Under Single Link Deletion [article]

Max Ward, Amitava Datta, Hung X. Nguyen, Jason Eshraghian
2022 arXiv   pre-print
The algorithm incorporates sophisticated and novel techniques, and generalises to the problem of computing the all-pairs shortest paths table after deleting each edge individually.  ...  More formally, given a graph, which edge after deletion disconnects the maximum number of pairs of vertices, where ties for number of pairs disconnected are broken by finding an edge that increases the  ...  We believe that a modified single-source shortest path algorithm can be used to find these critical edges efficiently when the graph has only positive edge weights.  ... 
arXiv:2108.06891v3 fatcat:a6eouyioijd5vnxunfbe3xuyeu

An Optimized All pair Shortest Paths Algorithm

Vijay Shankar Pandey, Rajendra Kumar, Dr. P K Singh
2010 International Journal of Computer Applications  
In this paper, we present an algorithm to compute all pairs optimized shortest paths in an unweighted and undirected graph with some additive error of at most 2.This algorithm can be extended for weighted  ...  The algorithm runs in n 5/2 ) times, where n is the number of vertices in the graph. This algorithm is much simpler than the existing algorithms.  ...  PREVIOUS WORK: ALL PAIRS SHORTEST PATH ALGORITHMS One of the most classical algorithm for computing all pairs shortest paths is F1oyd-Warshall algorithm [8] , which runs in O(n 3 ) time.  ... 
doi:10.5120/640-896 fatcat:xpjlvzdm5nbvfivb26z42dxnry

Algorithmic Techniques for Maintaining Shortest Routes in Dynamic Networks

Camil Demetrescu, Giuseppe F. Italiano
2007 Electronical Notes in Theoretical Computer Science  
In this paper, we survey algorithms for shortest paths in dynamic networks.  ...  Although research on this problem spans over more than three decades, in the last couple of years many novel algorithmic techniques have been proposed.  ...  In particular, King [19] presented a fully dynamic algorithm for maintaining all pairs shortest paths in directed graphs with positive integer weights less than C: the running time of her algorithm is  ... 
doi:10.1016/j.entcs.2006.11.006 fatcat:ss7kxtmk4fah5a5qmpxieln2be

An Efficient Algorithm for All Pair Shortest Paths

P K Singh, Rajendra Kumar, Vijay Shankar Pandey
2010 International Journal of Computer and Electrical Engineering  
In this paper, an all pairs optimized shortest path algorithm is presented for an unweighted and undirected graph with some additive error of at most 2.This algorithm can be extended for weighted graph  ...  The run time of the algorithm is of order Ο(n5/2), where n is the number of vertices present in the graph. This algorithm is much simpler than the existing algorithms.  ...  ALL PAIRS OPTIMIZED SHORTEST PATHS ALGORITHMS Aingworth et al. [1] gave the algorithm for all pairs shortest paths with additive error for unweighted and undirected graphs.  ... 
doi:10.7763/ijcee.2010.v2.263 fatcat:ihfyfbcifnd4pimsmrdvocpnci

Efficient Parameterized Algorithms for Computing All-Pairs Shortest Paths

Stefan Kratsch, Florian Nelles, Markus Bläser, Christophe Paul
2020 Symposium on Theoretical Aspects of Computer Science  
of algorithms for solving ALL-PAIRS SHORTEST PATHS.  ...  Computing all-pairs shortest paths is a fundamental and much-studied problem with many applications.  ...  In Section 3, we present the algorithm for vertex-weighted all-pairs shortest paths parameterized by the clique-width.  ... 
doi:10.4230/lipics.stacs.2020.38 dblp:conf/stacs/KratschN20 fatcat:qdig6y67mfddrerr5qjbid46fq

Comparative Study for Trends of Solving Single Source Shortest Path Problems

Nilanshi Nigam, Vivek Bhushan, Abdul Muttalib
2016 International Journal of Computer Applications  
As the name suggests, Single source shortest path is a technique to find the shortest path corresponding to a source vertex. Single source can be implemented using greedy and dynamic approach.  ...  There are many approaches proposed for the same. The idea is to minimize the complexity of the algorithm.  ...  of routing system in multipath graphs through Shortest Pairs of Arc-Disjoint P aths Problem (SADPP) algorithm for disjoint paths.  ... 
doi:10.5120/ijca2016908832 fatcat:7rj2kb4335h5tbh62gzygd4gcu
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