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More Algorithms for All-Pairs Shortest Paths in Weighted Graphs

2010
*
SIAM journal on computing (Print)
*

APSP

doi:10.1137/08071990x
fatcat:g6nnaexymra7zcqynpdkbhaz6q
*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? ...##
###
More algorithms for all-pairs shortest paths in weighted graphs

2007
*
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing - STOC '07
*

APSP

doi:10.1145/1250790.1250877
dblp:conf/stoc/Chan07
fatcat:hjvgkpode5cp7oarbre6fvynae
*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? ...##
###
Engineering Shortest Path Algorithms
[chapter]

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*. ...

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

1993
*
SIAM journal on computing (Print)
*

We investigate the

doi:10.1137/0222071
fatcat:wn3ogqqw4vc5bfsgcjeise6lqy
*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*. ...##
###
An Improved Algorithm for Finding All Pair Shortest Path

2012
*
International Journal of Computer Applications
*

Floyd Warshall's

doi:10.5120/7539-0492
fatcat:pxguyxviwbbgxndqd35picwahq
*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. ...##
###
Privacy Preservation in Social Network Analysis using Edge Weight Perturbation

2016
*
Indian Journal of Science and Technology
*

This is achieved by modification of

doi:10.17485/ijst/2016/v9i37/93810
fatcat:vxtle63abbfofmsmbj5n3mfmf4
*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. ...##
###
On the difficulty of some shortest path problems

2007
*
ACM Transactions on Algorithms
*

This also establishes a similar lower bound

doi:10.1145/1219944.1219951
fatcat:ernhz2cdmjhqnim5ht7ubbblme
*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. ...##
###
On the Difficulty of Some Shortest Path Problems
[chapter]

2003
*
Lecture Notes in Computer Science
*

This also establishes a similar lower bound

doi:10.1007/3-540-36494-3_31
fatcat:tceizql3cfeadfwcb6aiftuolu
*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. ...##
###
On the difficulty of some shortest path problems

2007
*
ACM Transactions on Algorithms
*

This also establishes a similar lower bound

doi:10.1145/1186810.1186815
fatcat:4msbqoswtzhk7nv7qdbhkntkfu
*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. ...##
###
Efficient Network Analysis Under Single Link Deletion
[article]

2022
*
arXiv
*
pre-print

The

arXiv:2108.06891v3
fatcat:a6eouyioijd5vnxunfbe3xuyeu
*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*. ...##
###
An Optimized All pair Shortest Paths Algorithm

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. ...

##
###
Algorithmic Techniques for Maintaining Shortest Routes in Dynamic Networks

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 ...

##
###
An Efficient Algorithm for All Pair Shortest Paths

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*. ...

##
###
Efficient Parameterized Algorithms for Computing All-Pairs Shortest Paths

2020
*
Symposium on Theoretical Aspects of Computer Science
*

of

doi:10.4230/lipics.stacs.2020.38
dblp:conf/stacs/KratschN20
fatcat:qdig6y67mfddrerr5qjbid46fq
*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. ...##
###
Comparative Study for Trends of Solving Single Source Shortest Path Problems

2016
*
International Journal of Computer Applications
*

As the name suggests, Single source

doi:10.5120/ijca2016908832
fatcat:7rj2kb4335h5tbh62gzygd4gcu
*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*. ...
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