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NC Algorithms for the Single Most Vital Edge Problem with Respect to All Pairs Shortest Paths

2000
*
Parallel Processing Letters
*

*For*a weighted, undirected graph G = V;E where jV j = n and jEj = m, w e examine

*the*

*single*

*most*

*vital*

*edge*

*with*

*respect*

*to*two measurements related

*to*all-pairs

*shortest*

*paths*APSP. ...

*The*

*Most*

*vital*

*edge*

*with*

*respect*

*to*

*the*diameter is

*the*

*edge*lying on such a u , v

*shortest*

*path*which when removed causes

*the*greatest increase in

*the*diameter. ... Venema et. al. 10 solved

*the*

*Single*

*Most*

*Vital*

*Edge*

*problem*

*with*

*respect*

*to*an s , t

*shortest*

*path*using this approach.

*To*solve MVE1 and MVE2 we extend

*the*result in 10 as follows. ...

##
###
NC algorithms for the single most vital edge problem with respect to all pairs shortest paths
[chapter]

1998
*
Lecture Notes in Computer Science
*

*For*a weighted, undirected graph G = V;E where jV j = n and jEj = m, w e examine

*the*

*single*

*most*

*vital*

*edge*

*with*

*respect*

*to*two measurements related

*to*all-pairs

*shortest*

*paths*APSP. ...

*The*

*Most*

*vital*

*edge*

*with*

*respect*

*to*

*the*diameter is

*the*

*edge*lying on such a u , v

*shortest*

*path*which when removed causes

*the*greatest increase in

*the*diameter. ... Venema et. al. 10 solved

*the*

*Single*

*Most*

*Vital*

*Edge*

*problem*

*with*

*respect*

*to*an s , t

*shortest*

*path*using this approach.

*To*solve MVE1 and MVE2 we extend

*the*result in 10 as follows. ...

##
###
NC ALGORITHMS FOR THE SINGLE MOST VITAL EDGE PROBLEM WITH RESPECT TO ALL PAIRS SHORTEST PATHS

2000
*
Parallel Processing Letters
*

*For*a weighted, undirected graph G = V;E where jV j = n and jEj = m, w e examine

*the*

*single*

*most*

*vital*

*edge*

*with*

*respect*

*to*two measurements related

*to*all-pairs

*shortest*

*paths*APSP. ...

*The*

*Most*

*vital*

*edge*

*with*

*respect*

*to*

*the*diameter is

*the*

*edge*lying on such a u , v

*shortest*

*path*which when removed causes

*the*greatest increase in

*the*diameter. ... Venema et. al. 10 solved

*the*

*Single*

*Most*

*Vital*

*Edge*

*problem*

*with*

*respect*

*to*an s , t

*shortest*

*path*using this approach.

*To*solve MVE1 and MVE2 we extend

*the*result in 10 as follows. ...

##
###
Page 7118 of Mathematical Reviews Vol. , Issue 97K
[page]

1997
*
Mathematical Reviews
*

| (5-GRIF-SI; Brisbane);
Suraweera, Francis (5-GRIF-SI; Brisbane)

*NC**algorithms**for**the**single**most**vital**edge**problem**with**respect**to**shortest**paths*. (English summary) Inform. Process. ... Summary: “*For*a weighted, undirected graph G = (VE),*the**single**most**vital**edge*in a network*with**respect**to**shortest**paths*is*the**edge*that, when removed, results in*the*greatest increase in*the**shortest*...##
###
Page 4201 of Mathematical Reviews Vol. , Issue 2001F
[page]

2001
*
Mathematical Reviews
*

)

*NC**algorithms**for**the**single**most**vital**edge**problem**with**respect**to*all pairs*shortest**paths*. ... Summary: “*For*a weighted, undirected graph G = (V, E) where |V|=n and |E|=™m, we examine*the**single**most**vital**edge**with**respect**to*all-pairs*shortest**paths*(APSP) under two different measurements. ...##
###
AORM: Fast Incremental Arbitrary-Order Reachability Matrix Computation for Massive Graphs

2021
*
IEEE Access
*

In particular,

doi:10.1109/access.2021.3077888
fatcat:dw6qm3xb65fsrpgqrh4uomoipi
*the*proposed method outperforms up*to*10 times compared*to*NetworkX*for*incremental allpairs*shortest**paths*computation. ... Processing a reachability query in large-scale networks using existing methods remains one of*the**most*challenging*problems*in graph mining. ... It is well known that*the*time complexity of BFS*for*finding*the**single*-source*shortest**paths*is O(n + m). Then, we can extend this*algorithm**for*all n nodes*to*compute*the*all-pair*shortest**paths*. ...##
###
Solving Systems of Difference Constraints Incrementally with Bidirectional Search

2004
*
Algorithmica
*

We propose an incremental

doi:10.1007/s00453-004-1081-6
fatcat:7mb7rpwr4vdffljzsorctbeory
*algorithm**for**the**problem*of maintaining systems of difference constraints. ...*The*major challenge is how*to*update*the*solution efficiently after*the*bidirectional search discovers a region that needs changes. ... We thank an anonymous referee*for*valuable suggestions that significantly improved*the*presentation of this paper. ...##
###
NC approximation algorithms for 2-connectivity augmentation in a graph
[chapter]

1997
*
Lecture Notes in Computer Science
*

We devise

doi:10.1007/bfb0002767
fatcat:fardrzra3nhqhi5tq4mor7y47m
*NC*approximation*algorithms**for**the*optimal 2-*edge*connectivity and*the*optimal 2-vertex connectivity augmentation*problems*by delivering solutions within (1 + In no)(1 + e) times optimum and ... Given an undirected graph G = (V, E0)*with*IVI--n, and a feasible set E of m weighted*edges*on V,*the*optimal 2-*edge*(2-vertex) connectivity augmentation*problem*is*to*find a subset S* __ E such that G ... Let*the**shortest**path*between bl and bk, denoted by Pbl,bk, be*the**shortest*among these 1-1*shortest**paths*, 2 < k < 1. ...##
###
Multicasting in cognitive radio networks: Algorithms, techniques and protocols

2014
*
Journal of Network and Computer Applications
*

Multicasting in CRNs is a challenging

doi:10.1016/j.jnca.2014.07.024
fatcat:xkjekyopd5fg5am3dhop36nadi
*problem*due*to**the*dynamic nature of spectrum opportunities available*to**the*SUs. ... In this paper, we provide a self-contained tutorial on*algorithms*and techniques useful*for*solving*the*multicast*problem*, and then provide a comprehensive survey of protocols that have been proposed*for*...*The*famous Dijkstra*algorithm*used*for*solving*the**shortest**path*tree (SPT)*problem*is an example greedy*algorithm*. ...##
###
New lower and upper bounds for shortest distance queries on terrains

2015
*
Proceedings of the VLDB Endowment
*

As

doi:10.14778/2850583.2850591
fatcat:jgjpsowh2fdz3nj6qsj2lu7oyu
*shortest*-*path*computation, an integral element of query processing, is inherently expensive on terrains, a key approach*to*enabling efficient query processing is*to*reduce*the*need*for*exact*shortest*-*path*...*To*view a copy of this license, visit http://creativecommons.org/licenses/by-*nc*-nd/4.0/.*For*any use beyond those covered by this license, obtain permission by emailing info@vldb.org. ... is at*most*7 times*the*optimal*shortest*surface*path*...##
###
PiP-X: Online feedback motion planning/replanning in dynamic environments using invariant funnels
[article]

2022
*
arXiv
*
pre-print

A volumetric funnel-graph is constructed using sampling-based methods, and an optimal funnel-

arXiv:2202.00772v1
fatcat:kqhkt6nfvndgbfyhzsxlbvbhpu
*path*from robot configuration*to*a desired goal region is then determined by computing*the**shortest*-*path*subtree ... We combine concepts from sampling-based methods, nonlinear systems analysis and control theory*to*create a*single*framework that enables feedback motion re-planning*for*any general nonlinear dynamical ... ACKNOWLEDGMENTS*The*authors are grateful*to**the*Robot Locomotion Group at MIT*for*providing an open-source software distribution*for*computing funnels. ...##
###
Modularity-based Backbone Extraction in Weighted Complex Networks
[article]

2022
*
arXiv
*
pre-print

*The*so-called "modularity

*vitality*backbone" removes nodes

*with*

*the*lower contribution

*to*

*the*network's modularity. ... Coarse-graining merges similar nodes

*to*reduce

*the*network size, while filter-based methods remove nodes or

*edges*according

*to*a specific statistical property. ... Previous works on modularity

*vitality*centrality has proved

*to*assign high scores

*to*

*the*

*most*influential nodes [32] .

*Algorithm*. ...

##
###
On Short Paths Interdiction Problems: Total and Node-Wise Limited Interdiction

2007
*
Theory of Computing Systems
*

In contrast,

doi:10.1007/s00224-007-9090-x
fatcat:tuygsdc3hbe43lsigtev4nsxsa
*the*short*paths*total interdiction*problem*is known*to*be NPhard. ... This is known as*the*short*paths*interdiction*problem*. ... We proceed*with*a negative observation. It is well known that*the*standard*shortest**path**problem*is in*NC*, that is it can be efficiently solved in parallel. ...##
###
On Short Paths Interdiction Problems: Total and Node-Wise Limited Interdiction

2007
*
Theory of Computing Systems
*

In contrast,

doi:10.1007/s00224-007-9025-6
fatcat:kiueed7ubjfzfchdem6abbfxta
*the*short*paths*total interdiction*problem*is known*to*be NPhard. ... This is known as*the*short*paths*interdiction*problem*. ... We proceed*with*a negative observation. It is well known that*the*standard*shortest**path**problem*is in*NC*, that is it can be efficiently solved in parallel. ...##
###
MODECP: A Multi-Objective Based Approach for Solving Distributed Controller Placement Problem in Software Defined Network

2022
*
Sensors
*

Moreover, compared

doi:10.3390/s22155475
pmid:35897980
pmcid:PMC9331998
fatcat:ydkybnjj75gazftbmhmgevxdzu
*with**the*genetic*algorithm*and random placement*algorithm*,*the*proposed*algorithm*performs better*with*low latency, high security, low load rate, and low link overhead. ... In*the*controller placement stage, an improved multi-objective differential evolution*algorithm*is proposed*to*search*for*controllers' positions and assign switches*to*controllers reasonably. ...*The**shortest**path*length is*the*combination of*the*number of hops of*the**shortest**path*and*the*length of*the**single*-hop physical link. ...
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