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A Lower Bound for the Shortest Path Problem

2001
*
Journal of computer and system sciences (Print)
*

This shows that

doi:10.1006/jcss.2001.1766
fatcat:lmh77vnl7fadzfbayiq7c3z3xa
*the*matrix-based repeated squaring algorithm*for**the**shortest**path**problem*is optimal in*the*unbounded fan-in PRAM model without bit operations. ... We show that*the**shortest**path**problem*cannot be solved in o(log n) time on an unbounded fan-in PRAM without bit operations using poly(n) processors, even when*the*bit-lengths of*the*weights on*the*edges ... ACKNOWLEGDMENTS We thank Dieter van Melkebeek, Varsha Dani, Soren Dayton, Marcus Schaefer, and Gina Steele*for*their help in proofreading*the*paper and suggesting valuable comments. ...##
###
A lower bound for the shortest path problem

*
Proceedings 15th Annual IEEE Conference on Computational Complexity
*

This shows that

doi:10.1109/ccc.2000.856731
dblp:conf/coco/MulmuleyS00
fatcat:e44jvkuykve2tmb2ugjqn34qpy
*the*matrix-based repeated squaring algorithm*for**the**shortest**path**problem*is optimal in*the*unbounded fan-in PRAM model without bit operations. ... We show that*the**shortest**path**problem*cannot be solved in o(log n) time on an unbounded fan-in PRAM without bit operations using poly(n) processors, even when*the*bit-lengths of*the*weights on*the*edges ... ACKNOWLEGDMENTS We thank Dieter van Melkebeek, Varsha Dani, Soren Dayton, Marcus Schaefer, and Gina Steele*for*their help in proofreading*the*paper and suggesting valuable comments. ...##
###
On the difficulty of some shortest path problems

2007
*
ACM Transactions on Algorithms
*

We prove super-linear

doi:10.1145/1219944.1219951
fatcat:ernhz2cdmjhqnim5ht7ubbblme
*lower**bounds**for*some*shortest**path**problems*in directed graphs, where no such*bounds*were previously known. ... 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 ...*A**lower**bound**for**the*k-pairs*shortest**paths**problem*Our k-pairs*shortest**paths**lower**bound*is based on*the**lower**bound*construction of Karger, Koller, and Phillips [13] . ...##
###
On the Difficulty of Some Shortest Path Problems
[chapter]

2003
*
Lecture Notes in Computer Science
*

We prove super-linear

doi:10.1007/3-540-36494-3_31
fatcat:tceizql3cfeadfwcb6aiftuolu
*lower**bounds**for*some*shortest**path**problems*in directed graphs, where no such*bounds*were previously known. ... 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 ...*A**lower**bound**for**the*k-pairs*shortest**paths**problem*Our k-pairs*shortest**paths**lower**bound*is based on*the**lower**bound*construction of Karger, Koller, and Phillips [13] . ...##
###
On the difficulty of some shortest path problems

2007
*
ACM Transactions on Algorithms
*

We prove super-linear

doi:10.1145/1186810.1186815
fatcat:4msbqoswtzhk7nv7qdbhkntkfu
*lower**bounds**for*some*shortest**path**problems*in directed graphs, where no such*bounds*were previously known. ... 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 ...*A**lower**bound**for**the*k-pairs*shortest**paths**problem*Our k-pairs*shortest**paths**lower**bound*is based on*the**lower**bound*construction of Karger, Koller, and Phillips [13] . ...##
###
Adaptations of the A* algorithm for the computation of fastest paths in deterministic discrete-time dynamic networks

2002
*
IEEE transactions on intelligent transportation systems (Print)
*

These

doi:10.1109/6979.994796
fatcat:rcnja5ga55fephcdrhasksyxya
*lower**bounds*are exploited in designing efficient adaptations of*the**A** algorithm to solve instances of*the*one-to-one dynamic fastest*path**problem*. ... This paper extends*the**A** methodology to*shortest**path**problems*in dynamic networks, in which arc travel times are time dependent. ...*For**the*one-to-one*shortest**path**problem**for*all departure times, two dynamic adaptations of*the**A** algorithm are possible, using*the*static*lower**bounds*or*the*mixed*lower**bounds*. ...##
###
Lagrangian Relaxation for the Multiple Constrained Robust Shortest Path Problem

2019
*
Mathematical Problems in Engineering
*

Nonlinear optimization model is developed to model constrained robust

doi:10.1155/2019/3987278
fatcat:iz4yjehrn5e2jhxdhr7fi6tl5i
*shortest**path**problem*.*The*dual nature of*the*proposed*problem*is deduced based on*the*Lagrangian duality theory. ...*The*study focuses on*a*multiple constrained reliable*path**problem*in which travel time reliability and resource constraints are collectively considered. ... GXL2015031, to which*the*author is very grateful. ...##
###
Algorithms for Non-Linear and Stochastic Resource Constrained Shortest Paths
[article]

2017
*
arXiv
*
pre-print

*The*main contribution of this paper is to introduce

*a*standard procedure to generate

*bounds*on

*paths*resources in

*a*general setting which covers most resource constrained

*shortest*

*path*

*problems*, among ... Resource constrained

*shortest*

*path*

*problems*are usually solved thanks to

*a*smart enumeration of all

*the*non-dominated

*paths*. ... Acknowledgments I greatly thank my PhD advisor Frédéric Meunier

*for*his numerous and deep remarks on

*the*mathematics and

*the*way to write this article. ...

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

1993
*
SIAM journal on computing (Print)
*

Finally, we prove an (mn)

doi:10.1137/0222071
fatcat:wn3ogqqw4vc5bfsgcjeise6lqy
*lower**bound*on*the*running time of any*path*-comparison-based algorithm*for**the*allpairs*shortest**paths**problem*. ... We investigate*the*all-pairs*shortest**paths**problem*in weighted graphs. ... 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. ...##
###
Running time analysis of Ant Colony Optimization for shortest path problems

2012
*
Journal of Discrete Algorithms
*

We present

doi:10.1016/j.jda.2011.06.002
fatcat:kia3okeal5d2vfqm3vunpxtske
*bounds*on*the*running time of different ACO systems*for**shortest**path**problems*. ... Our upper*bound*is asymptotically tight*for*large evaporation factors, holds with high probability, and transfers to*the*all-pairs*shortest**paths**problem*. ... Acknowledgements Dirk Sudholt was partly supported by EPSRC grant EP/D052785/1 and*a*postdoctoral fellowship from*the*German Academic Exchange Service while visiting*the*International Computer Science ...##
###
On the Quadratic Shortest Path Problem
[chapter]

2015
*
Lecture Notes in Computer Science
*

In this paper we model these situations as

doi:10.1007/978-3-319-20086-6_29
fatcat:e3e56wgofjcpbel42p4ntx52i4
*a*Quadratic*Shortest**Path**Problem*, which calls*for**the*minimization of*a*quadratic objective function subject to*shortest*-*path*constraints. ... Based on this special case and*problem*structure, we devise fast*lower**bounding*procedures*for**the*general*problem*and show computationally that they clearly outperform other approaches proposed in*the*... Once z e has been computed*for*each e ∈*A*,*the*GL*bound*is given by*the*solution to*the*following*shortest**path**problem*: LB GLT = min e∈*A*(z e + c e )x e : x ∈ X st . ...##
###
Fast Robust Shortest Path Computations

2018
*
Algorithmic Approaches for Transportation Modeling, Optimization, and Systems
*

This methods generalizes to binary linear robust

doi:10.4230/oasics.atmos.2018.5
dblp:conf/atmos/HansknechtRS18
fatcat:6k52ynz7gjhhjpvwagdgw3b7ny
*problems*. Specifically*for**shortest**paths*we derive*a**lower**bound*to speed-up*the*Divide and Conquer of Θ. ... In*the*robust*shortest**path**problem*we are given an s-t-graph D(V,*A*) and*for*each arc*a*nominal length c(*a*) and*a*maximal increase d(*a*) of its length. ... We give an efficient method to obtain*lower**bounds**for**the*length of*shortest**paths*with respect to c θ . We use these*bounds*to speed up*the*Divide and Conquer approach. ...##
###
A generalized permanent label setting algorithm for the shortest path between specified nodes

1972
*
Journal of Mathematical Analysis and Applications
*

ACKNOWLEDGIVIENT I IvYant to thank Guy de Ghellinck

doi:10.1016/0022-247x(72)90091-1
fatcat:534zjw2ru5acnit65372evxsti
*for*several helpful suggestions. ... NEMH.4USER*The*identification of*the*h(i) as*lower**bounds*on*the*length of*a**shortest**path*from i to 11 suggests*a*method*for*determining*the*h(i). ... Thus,*the*h(i) are*lower**bounds*on*the*length of*a**shortest**path*from i to 71. In our algorithm,*the*nodes are permanently labeled in order of increasing O(i)+ h(i). ...##
###
Finding All Hops Shortest Paths

2004
*
IEEE Communications Letters
*

*The*AHSP

*problem*involves selecting,

*for*all hop counts,

*the*

*shortest*

*paths*from

*a*given source to any other node in

*a*network. ... In this letter, we introduce and investigate

*a*new

*problem*referred to as

*the*All Hops

*Shortest*

*Paths*(AHSP)

*problem*. ... Next, we provide

*a*tight

*lower*

*bound*on

*the*worst-case computational complexity of

*the*optimal comparison-based solution to AHSP based on Theorem 1. ...

##
###
Running Time Analysis of ACO Systems for Shortest Path Problems
[chapter]

2009
*
Lecture Notes in Computer Science
*

We analyze

doi:10.1007/978-3-642-03751-1_6
fatcat:ljzdzmeq7jefrfinfa4haifdwy
*the*running time of different ACO systems*for**shortest**path**problems*. ... Our upper*bound*is asymptotically tight*for*large evaporation factors, holds with high probability, and transfers to*the*all-pairs*shortest**paths**problem*. ... Consider*a*pair (u, v) of vertices. Let ℓ u,v denote*the*maximum number of edges of*a**shortest**path*from u to v. ...
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