The Internet Archive has a preservation copy of this work in our general collections.
The file type is `application/pdf`

.

## Filters

##
###
Faster Replacement Paths
[article]

2010
*
arXiv
*
pre-print

The

arXiv:1007.2216v1
fatcat:pvxa43lspfavjmviiii7ry6ga4
*replacement**paths*problem for*directed**graphs*is to find for given nodes s*and*t*and*every edge e on the*shortest**path*between them, the*shortest**path*between s*and*t which avoids e. ... Our result shows that, at least for small integer weights, the*replacement**paths*problem*in**directed**graphs*may be easier than the related all pairs*shortest**paths*problem*in**directed**graphs*, as the current ... For*unweighted**graphs*, both the*replacement**paths*problem*and*the second*shortest**simple**path*problem are closely related to Boolean matrix multiplication; for general*directed**graphs*with arbitrary weights ...##
###
Near Optimal Algorithm for the Directed Single Source Replacement Paths Problem

2020
*
International Colloquium on Automata, Languages and Programming
*

*In*the Single Source

*Replacement*

*Paths*(SSRP) problem we are given a

*graph*G = (V, E),

*and*a

*shortest*

*paths*tree

*K̂*rooted at a node s,

*and*the goal is to output for every node t ∈ V

*and*for every edge ... e

*in*

*K̂*the length of the

*shortest*

*path*from s to t avoiding e. ... The

*k*

*shortest*

*simple*

*paths*problem can be solved by invoking the

*replacement*

*paths*algorithm

*k*times

*and*adding a very small weight to the

*path*found

*in*each invocation. ...

##
###
Faster replacement paths
[chapter]

2011
*
Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms
*

The

doi:10.1137/1.9781611973082.102
dblp:conf/soda/Williams11
fatcat:aanila5k6fdjzk4n2lu6ztguye
*replacement**paths*problem for*directed**graphs*is to find for given nodes s*and*t*and*every edge e on the*shortest**path*between them, the*shortest**path*between s*and*t which avoids e. ... Our result shows that, at least for small integer weights, the*replacement**paths*problem*in**directed**graphs*may be easier than the related all pairs*shortest**paths*problem*in**directed**graphs*, as the current ... The author would like to thank Ryan Williams for his moral support*and*the anonymous reviewers for their valuable input. ...##
###
Minimum Cuts and Shortest Cycles in Directed Planar Graphs via Noncrossing Shortest Paths

2017
*
SIAM Journal on Discrete Mathematics
*

Let $G$ be an $n$-node

doi:10.1137/16m1057152
fatcat:s6osvpbcwjeydpmcmfmuncq7k4
*simple**directed*planar*graph*with nonnegative edge weights. ... The kernel of our result is an $O(n\log\log n)$-time algorithm for computing noncrossing*shortest**paths*among nodes well ordered on a common face of a*directed*plane*graph*, which is extended from the algorithm ... a*shortest*cycle*in**unweighted**directed*planar G*in*o(n 3/2 ) time. ...##
###
Fine-Grained Complexity and Conditional Hardness for Sparse Graphs
[article]

2017
*
arXiv
*
pre-print

Our sparse reductions for

arXiv:1611.07008v3
fatcat:vuwsyquqn5bwlp2kyx7iks5wxi
*directed**path*problems*in*the $\tilde{O}(mn)$ class establish that several problems*in*this class, including 2-SiSP (second*simple**shortest**path*), Radius,*and*Eccentricities, ...*in*the*graph*, the length of a longest*shortest**path*starting at that vertex. ... Hence, the*k*-th*shortest**path**in*the collection of*k*-SiSPs from x 0,i to x 1,i*in*log n G i , 1 ≤ i ≤ ⌈log n⌉ (after removing duplicates), corresponds to the*k*-th SiSC passing through x. ...##
###
On Dynamic Shortest Paths Problems
[chapter]

2004
*
Lecture Notes in Computer Science
*

*directed*or undirected

*graphs*, are,

*in*a strong sense, at least as hard as the static all-pairs

*shortest*-

*paths*problem. ... (ii) A randomized fully-dynamic algorithm for the all-pairs shortestpaths problem

*in*

*directed*

*unweighted*

*graphs*with an amortized update time ofÕ(m √ n)

*and*a worst case query time is O(n 3/4 ). ... There is a decremental algorithm for maintaining the first

*k*levels of a single-source

*shortest*-

*paths*tree,

*in*a

*directed*or undirected

*unweighted*

*graph*, whose total running time, over all deletions, is ...

##
###
On Dynamic Shortest Paths Problems

2010
*
Algorithmica
*

*directed*or undirected

*graphs*, are,

*in*a strong sense, at least as hard as the static all-pairs

*shortest*-

*paths*problem. ... (ii) A randomized fully-dynamic algorithm for the all-pairs shortestpaths problem

*in*

*directed*

*unweighted*

*graphs*with an amortized update time ofÕ(m √ n)

*and*a worst case query time is O(n 3/4 ). ... There is a decremental algorithm for maintaining the first

*k*levels of a single-source

*shortest*-

*paths*tree,

*in*a

*directed*or undirected

*unweighted*

*graph*, whose total running time, over all deletions, is ...

##
###
Finding k Simple Shortest Paths and Cycles
[article]

2016
*
arXiv
*
pre-print

The problem of finding multiple

arXiv:1512.02157v2
fatcat:nxxmrpjor5hilbx5p66ggmuzu4
*simple**shortest**paths**in*a weighted*directed**graph*$G=(V,E)$ has many applications,*and*is considerably more difficult than the corresponding problem when cycles are allowed ... We also give hardness results for sparse*graphs*, relative to the complexity of computing a minimum weight cycle*in*a*graph*, for several variants of problems related to finding $*k*$*simple**paths**and*cycles ... For*unweighted**directed**graphs*, Roditty*and*Zwick [29] gave anÕ(km √ n) randomized algorithm for*k*-SiSP. ...##
###
Tight Hardness for Shortest Cycles and Paths in Sparse Graphs
[chapter]

2018
*
Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
*

*Replacement*

*Paths*, Second

*Shortest*

*Paths*,

*and*so on. ...

*graph*, • Second

*Shortest*

*Path*

*in*a

*directed*weighted

*graph*, • Betweenness Centrality of a given node

*in*a

*directed*weighted

*graph*. ... Landsberg

*and*Mateusz Michalek for valuable discussions about tensor rank lower bounds. We would like to thank the anonymous reviewers whose suggestions we implemented. ...

##
###
Restoration by path concatenation: fast recovery of MPLS paths

2002
*
Distributed computing
*

The theory pertains to restoration of

doi:10.1007/s00446-002-0080-6
fatcat:tts3nnjkxnh6jer6r3bumd5wb4
*shortest**paths**in*a network following failure, e.g., we prove that a*shortest**path**in*a network after removing*k*edges is the concatenation of at most*k*+ 1*shortest*...*paths**in*the original network. ... We thank Noga Alon for simplifying the proof of the existence of a set B of bypass*paths**in*the proof of Theorem 1. ...##
###
Near Optimal Algorithm for the Directed Single Source Replacement Paths Problem
[article]

2020
*
arXiv
*
pre-print

*In*the Single Source

*Replacement*

*Paths*(SSRP) problem we are given a

*graph*$G = (V, E)$,

*and*a

*shortest*

*paths*tree $\widehat{

*K*}$ rooted at a node $s$,

*and*the goal is to output for every node $t \

*in*V$ ...

*and*for every edge $e$

*in*$\widehat{

*K*}$ the length of the

*shortest*

*path*from $s$ to $t$ avoiding $e$. ... Also, note that any

*path*from goes from x 1 to a i

*and*then preforms a 3 vertex

*path*: If α i,j < 8L − 7i + 5 then

*k*must be a index which minimizes the length of this 3 vertex

*path*. ...

##
###
Tight Hardness for Shortest Cycles and Paths in Sparse Graphs
[article]

2020
*
arXiv
*
pre-print

), Radius,

arXiv:1712.08147v4
fatcat:4kmi3ia3d5cmriclwvyj6oynwa
*Replacement**Paths*, Second*Shortest**Paths*,*and*so on. ... ,*Replacement**Paths**in*a*directed*weighted*graph*, Second*Shortest**Path**in*a*directed*weighted*graph*, Betweenness Centrality of a given node*in*a*directed*weighted*graph*. ... We thank Pawel Gawrychowski for pointing out a typo*in*a previous version of the paper. ...##
###
Deterministic Combinatorial Replacement Paths and Distance Sensitivity Oracles
[article]

2019
*
arXiv
*
pre-print

For the

arXiv:1905.07483v1
fatcat:bk4olmgm6fdpdn3tk2jgmaelpm
*replacement**paths*problem, let G = (V,E) be a*directed**unweighted**graph*with n vertices*and*m edges*and*let P be a*shortest**path*from s to t*in*G. ... The {\sl*replacement**paths*} problem is to find for every edge e \*in*P the*shortest**path*from s to t avoiding e. ... For*directed**unweighted**graphs*, the randomized*replacement**paths*algorithm of Roditty*and*Zwick [37] implies that the*k**simple**shortest**paths*has a randomized O(km √ n) time algorithm. ...##
###
Subcubic Equivalences between Path, Matrix and Triangle Problems

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

Finding the second

doi:10.1109/focs.2010.67
dblp:conf/focs/WilliamsW10
fatcat:3h7a5os4vjbk3hqktxahtbe4bm
*shortest**simple**path*between two nodes*in*a weighted digraph. Note the only previously known equivalence*in*the above was that of (1)*and*(2) . ... Finding a minimum weight cycle*in*a*graph*of non-negative edge weights. 8. The*replacement**paths*problem on weighted digraphs. 9. ...*In*ESA, pages 580-591, 2004. [RZ05] L. Roditty*and*U. Zwick.*Replacement**paths**and**k**simple**shortest**paths**in**unweighted**directed**graphs*.*In*Proc. ICALP, volume 32, pages 249-260, 2005. [Spi03] J. P. ...##
###
Efficiently listing bounded length st-paths
[article]

2014
*
arXiv
*
pre-print

The problem of listing the $

arXiv:1411.6852v1
fatcat:k3jivx57szhmfmx6hpnwpb5nea
*K*$*shortest**simple*(loopless) $st$-*paths**in*a*graph*has been studied since the early 1960s. ... For a non-negatively weighted*graph*with $n$ vertices*and*$m$ edges, the most efficient solution is an $O(*K*(mn + n^2 \log n))$ algorithm for*directed**graphs*by Yen*and*Lawler [Management Science, 1971 ... Algorithm 4 using a binary heap outputs all α-bounded st-*paths**in*increasing order of their lengths*in*O((nt(n, m) + log γ)γ) total time, using O(mγ) space. ...
« Previous

*Showing results 1 — 15 out of 3,909 results*