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All-Pairs Shortest Paths in O(n²) Time with High Probability

2010
*
2010 IEEE 51st Annual Symposium on Foundations of Computer Science
*

*in*expectation and

*with*

*high*

*probability*. ... The analysis relies on a proof that the number of locally

*shortest*

*paths*

*in*such randomly weighted graphs is

*O*(n 2 ),

*in*expectation and

*with*

*high*

*probability*. ... Furthermore, our algorithm runs

*in*

*O*(n 2 )

*time*

*with*

*high*

*probability*and works for both directed and undirected versions of the

*all*-

*pairs*

*shortest*

*paths*problem. ...

##
###
All-pairs shortest paths inO(n2) time with high probability

2013
*
Journal of the ACM
*

*in*expectation and

*with*

*high*

*probability*. ... The analysis relies on a proof that the number of locally

*shortest*

*paths*

*in*such randomly weighted graphs is

*O*(n 2 ),

*in*expectation and

*with*

*high*

*probability*. ... Furthermore, our algorithm runs

*in*

*O*(n 2 )

*time*

*with*

*high*

*probability*and works for both directed and undirected versions of the

*all*-

*pairs*

*shortest*

*paths*problem. ...

##
###
Faster Walks in Graphs: AÕ(n2) Time-Space Trade-off for Undirecteds-tConnectivity
[chapter]

2013
*
Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms
*

As our main result, we propose a family of randomized algorithms for USTCON which achieves a

doi:10.1137/1.9781611973105.133
dblp:conf/soda/Kosowski13
fatcat:4mgoz2t5grb5hpcxofdy6jaxhi
*time*-space product of S·T =*O*(n 2 )*in*graphs*with*n nodes and m edges (where the*O*-notation disregards poly-logarithmic ...*In*particular, we obtain an algorithm running*in**time**O*(n + m) which is,*in*general, more space-efficient than both BFS and DFS. ... Since the*path*P s = (i 0 , i 1 , . . . , i a−1 ) is a*shortest**path**in*graph G between nodes i 0 and i a−1 , such that P s ⊆ A and Γ(P s ) ⊆ A, it follows that (cf. ...##
###
Optimality Bounds of the Connectivity of Adhoc Networks with Beamforming Antennas

2009
*
GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference
*

Adhoc networks will play an important role

doi:10.1109/glocom.2009.5425735
dblp:conf/globecom/KieseHV09
fatcat:sv76wdf2yrdevhv63fmylr35vq
*in*future access networks. Previous studies have shown, that the connectivity of such networks can be notably increased by employing directional antennas. ... This work tries to close this gap by providing a method to calculate provable bounds on the connectivity of an adhoc network*with*keyhole antennas and a variety of secondary optimization criteria via Mixed ... Finding these*paths*can be interpreted as a classic*shortest**path*problem (solvable by polynomial algorithms like Dijkstra's Algorithm [2] ),*with*link weights σ e : If the total cost of the*shortest*...##
###
Edge-disjoint paths revisited

2007
*
ACM Transactions on Algorithms
*

The approximability of the maximum edge disjoint

doi:10.1145/1290672.1290683
fatcat:7vyztvdf7rfwxcnfdfkdgzhjbe
*paths*problem (EDP)*in*directed graphs was seemingly settled by the fl(ml/2-e)-hardness result of Guruswami et al. [10] and the*O*(x/~ ) approximation achievable ... Our results also extend to EDP*with*weights and to the unsplittable flow problem*with*uniform edge capacities. ... The algorithm simply considers the*shortest**path*length for each unrouted (si, ti)*pair*and connects a*pair**with*minimum*shortest**path*length via its*shortest**path*. ...##
###
A new algorithm to find the shortest paths between all pairs of nodes

1982
*
Discrete Applied Mathematics
*

A new algorithm to find the

doi:10.1016/0166-218x(82)90031-2
fatcat:7l4g7vost5dshom2k543jcwgbu
*shortest**paths*between*all**pairs*of nodes is presented. This algorithm makes use of a dual cost transformation and of a particular data structure. ... Its worst case*time*complexity is of the order of the third power of the number of nodes, and its space complexity is linear*with*the number of arcs. ...*In*such models usually the*shortest**paths*between*all*Origin-Destination*pairs*need to be determined many*times*,*with*different values of arc lengths. ...##
###
Shortest path problems with node failures

1992
*
Networks
*

Consider the problem of finding the

doi:10.1002/net.3230220607
fatcat:6gdjerhfgneltowadhdqfiw45y
*shortest**paths*from a node source s to a node sink t*in*a complete network. ... We first show that the problem is,*in*general, NPhard and then we develop polynomial*time*procedures for special cases of it. ... the*path**with*maximum*probability*of being the*shortest*, or finding the*path**with*minimum variance among the*shortest*, etc. ...##
###
Performance evaluation of ATM shortcut connections in overlaid IP/ATM networks

1999
*
IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320)
*

These experiments indicate that

doi:10.1109/infcom.1999.752169
dblp:conf/infocom/FiroiuKT99
fatcat:vmctzqjaefcbjn5ig65u7yxe7e
*in*many cases the utilization of an IP/ATM network increases proportionally to the decrease*in*the average*path*length when ATM shortcuts are used. ... We model an IP/ATM network*with*and without ATM shortcuts as two loss networks. ... The 1P tlows can be routed*in*two ways: one is over the*shortest**path**in*the 1P network following the*path*of each 1P link*in*the ATM network; the other is over the*shortest**path**in*ATM network (i.e., ...##
###
Resource discovery in distributed networks

1999
*
Proceedings of the eighteenth annual ACM symposium on Principles of distributed computing - PODC '99
*

The total number of connections required is

doi:10.1145/301308.301362
dblp:conf/podc/Harchol-BalterLL99
fatcat:ujiru2pgafeexo6pm3aulcqeve
*O*(n log2 n) and the total number of pointers which must be communicated is*O*(*n2*log2 n),*with**high**probability*. ... We propose a very simple algorithm called Name-Dropper whereby*all*machines learn about each other within*O*(log' n) rounds*with**high**probability*, where n is the number of machines*in*the network. ... Then we're done by the following argument: Pick one*shortest**path*between each of the*n2**pairs*of nodes. Each of these*shortest**paths*has at most n triples. ...##
###
Additive Spanners in Nearly Quadratic Time
[chapter]

2010
*
Lecture Notes in Computer Science
*

*With*

*probability*≥ 1 − 1/n, H is an additive (2k + 4 )-spanner. Proof. Fix a

*pair*{a, b} of vertices

*in*G and a

*shortest*

*path*P between them. ... Fix a

*pair*{a, b} of vertices

*in*G, and fix any

*shortest*

*path*P from a to b

*in*G

*with*the fewest heavy edges. ...

##
###
Monitoring path nearest neighbor in road networks

2009
*
Proceedings of the 35th SIGMOD international conference on Management of data - SIGMOD '09
*

*In*the searching phase, the BNE finds the

*shortest*

*path*to the destination, during which a candidate set that guarantees to include the k -PNN is generated at the same

*time*. ... Given a destination where a user is going to, this new query returns the k -NN

*with*respect to the

*shortest*

*path*connecting the destination and the user's current location, and thus provides a list of ...

*High*deviation implies that the user usually does not choose the

*shortest*

*path*and an update of the whole k -PNN is required each

*time*the user deviates. ...

##
###
Local Link Protection Scheme in IP Networks
[chapter]

2007
*
Lecture Notes in Computer Science
*

*In*this paper, we proposed an IP Local Link-Protection (IPLLP) scheme based on the characteristic of

*shortest*-

*path*routing

*in*IP networks. ...

*In*the simulation results, we observe that IP Local Link-Protection scheme can efficiently improve network survivability

*in*a small-scale and

*high*-degree network. ... Second,

*all*scenarios of each link failure are simulated, and

*all*

*O*-D

*pairs*are tested according to the present routing tables. ...

##
###
Multiple Source Replacement Path Problem
[article]

2020
*
arXiv
*
pre-print

When there are $n$ sources, the combinatorial algorithm of (Bernstein and Karger, STOC 2009) can be used to find

arXiv:2005.09262v2
fatcat:imfmm3usrfalni4jcuj4cdm2ce
*all**pair*replacement*path**in*$\tilde*O*(mn + n^3)$*time*. ...*in*$\tilde*O*(m+n)$*time*. ... Also, d(s, t) will denote the length of the*shortest*st*path*. Formally, d(s, t) = d(s, t, ) = |st|. • The term*with*a*high**probability*means*with*a*probability*≥ 1 − 1 n c where c ≥ 1. ...##
###
Packet Routing with Genetically Programmed Mobile Agents
[chapter]

2000
*
Telecommunication Network Intelligence
*

The result is a

doi:10.1007/978-0-387-35522-1_22
dblp:conf/smartnet/SchuringaR00
fatcat:k4bfplnfyjbqfjyqbkchdzght4
*high*performance, self-configuring routing method, irrespective of the network topology and traffic. ... We use genetic programming to build mobile agents that monitor the network status and set the routing tables*in*the network nodes*in*such a way that it maximizes network throughput and minimizes the overall ... To compute the*shortest**path*between*all**pairs*has computational complexity*O*(*N2*). ...##
###
Utility-based forwarding

2012
*
Proceedings of the third ACM international workshop on Mobile Opportunistic Networks - MobiOpp '12
*

Several proposals are available

doi:10.1145/2159576.2159585
dblp:conf/mobiopp/Pagani012
fatcat:hbz6prcrabbqflw6mfexenxxru
*in*the literature that deal*with*the problem of message forwarding*in*Opportunistic Networks (ONs). ... These proposals attempt to derive the*path*from source to destination that minimizes delivery latency and traveled hops, and maximizes the*probability*of successful delivery, while saving the overall system ... latency of*O**path*. ...
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