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Algorithms for Non-Linear and Stochastic Resource Constrained Shortest Paths
[article]

2017
*
arXiv
*
pre-print

Recent improvements of these enumeration algorithms rely

arXiv:1504.07880v2
fatcat:4up4vrxudfa3fmgxx6gzhgkd24
*on**the*use of*bounds**on**path*resources to discard partial solutions.*The*quality of*the**bounds*determines*the*performance of*the*algorithm. ...*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 ... 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. ...##
###
Computing Shortest Paths Using A*, Landmarks, and Polygon Inequalities (Abstract)
[article]

2016
*
arXiv
*
pre-print

This heuristic's benefits are permitted by a new approach for computing

arXiv:1603.01607v1
fatcat:izoxkc3ovbajrkdash3vhpln2a
*lower**bounds*using generalized polygon inequalities, leveraging distance information from two landmarks as opposed to*the*common ... We introduce a new heuristic for*the*A* algorithm that references a data structure much smaller than*the**one*required by*the*ALT heuristic. ... Laszlo, my doctoral committee at*the*Nova Southeastern University GSCIS and my employer, Raytheon BBN Technologies for their support throughout*the*Computer Science PhD program. ...##
###
Distributed Processing of k Shortest Path Queries over Dynamic Road Networks
[article]

2022
*
arXiv
*
pre-print

However, most existing approaches are designed to identify KSPs

arXiv:2004.02580v3
fatcat:czasqu4ngbhpdi2fh23ysl2dcm
*on*a static graph in a sequential manner (i.e.,*the*(i+1)-th*shortest**path*is generated based*on**the*i-th*shortest**path*), restricting their ... We therefore propose KSP-DG, a*distributed*algorithm for identifying k-*shortest**paths*in a dynamic graph. ...*Lower**Bound*Distances After identifying*the*set of*bounding**paths*between 𝑣 𝑖 and 𝑣 𝑗 in subgraph 𝑆𝐺, we aim to determine*the**bounding**path*that would impose as tight a*lower**bound**on**the**shortest*...##
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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. ...##
###
Estimation of Shortest Path Covariance Matrices
[article]

2020
*
arXiv
*
pre-print

In particular, we focus

arXiv:2011.09986v1
fatcat:2mortzq7hraerhe36jkgdkfade
*on**shortest**path*covariance matrices, where*the*covariance between any two measurements is determined by*the**shortest**path*distance in an underlying graph with d nodes. ... We also give an information theoretic*lower**bound*matching our upper*bound*up to a factor D and discuss some directions towards closing this gap. ...*Lower**Bound*We now prove a simple*lower**bound**on**the*sample complexity of*shortest**path*covariance estimation when a fixed subset of entries S (e.g., corresponding to a sparse ruler) are read in each sample ...##
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Brief Announcement: Near Optimal Bounds for Replacement Paths and Related Problems in the CONGEST Model

2022
*
Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing
*

We present round complexity results in

doi:10.1145/3519270.3538473
fatcat:s3b2sphdp5ehvocrsuykmaoqyi
*the*CONGEST model for Replacement*Paths*(RPaths), Minimum Weight Cycle (MWC), and All Nodes*Shortest*Cycles (ANSC). ... We also present*lower*and upper*bounds*for approximation: a (2 − (1/𝑔))-approximation algorithm for undirected unweighted MWC that runs in Õ ( √ 𝑛 + 𝐷) rounds, improving*on**the*previous best*bound*of ... This algorithm has sublinear round complexity when 𝐷 is õ (𝑛 3/4 ) and compares favorably with our Ω(𝑛)*lower**bound*for (2 − 𝜖)approximation of undirected weighted MWC. ...##
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A nearly optimal distributed algorithm for computing the weighted girth

2021
*
Science China Information Sciences
*

Instead of computing all pairs

doi:10.1007/s11432-020-2931-x
fatcat:eg4vwzqa75axrbzevgoz356yzm
*shortest**paths*, our algorithm can always find a range to*bound**the*weighted girth and narrow*the*range by*the*modified*distributed*BFS with a distance constraint. ... These two algorithms are based*on*computing*distributed*APSP in unweighted graphs. Refs. [10, 15] showed that*the**lower**bound*of computing APSP in unweighted graphs is Ω(n/ log n + D). ...*Lower**bound*In this section, we give an Ω(D + n/ log n) rounds*lower**bound*for*distributively*computing*the*weighted girth under*the*CON GEST model, based*on**the*reduction technique from [16] . ...##
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A Simple Ant Colony Optimizer for Stochastic Shortest Path Problems

2011
*
Algorithmica
*

*The*question is whether

*the*ants can find or approximate

*shortest*

*paths*in

*the*presence of noise. We characterize instances where

*the*ants can discover

*the*real

*shortest*

*paths*efficiently. ...

*The*behavior of

*the*ant system changes dramatically when

*the*noise is perfectly correlated as then

*the*ants find

*shortest*

*paths*efficiently. ... Acknowledgments

*The*authors thank Samitha Samaranayake and Sébastien Blandin from UC Berkeley for references and discussions

*on*stochastic

*shortest*

*path*problems and Thomas Sauerwald for pointing us to ...

##
###
A lower bound on the expected optimal value of certain random linear programs and application to shortest paths and reliability
[article]

2016
*
arXiv
*
pre-print

Under reasonable assumptions, this problem is reduced to studying

arXiv:1504.00865v2
fatcat:7skh7j4l6zhdzg66y3pmpq6fii
*the*expectation of*the*length of*the**shortest**path*in*the*directed degradation graph of*the*systems where*the*parameters are given by a ...*The*expectation itself being sometimes out of reach, in closed form or even through Monte Carlo simulations in*the*case of large systems, we propose an easily computable*lower**bound*. ...*The*goal of this paper is to propose a*lower**bound**on**the*expected length of*the**shortest**path*.*The*paper is organized as follows. ...##
###
A new bound for the midpoint solution in minmax regret optimization with an application to the robust shortest path problem

2015
*
European Journal of Operational Research
*

To illustrate

doi:10.1016/j.ejor.2015.02.023
fatcat:mn4q6exagzghzeh6v45lzrs4em
*the*quality of*the*proposed*bound*, we use it within a branch and*bound*framework for*the*robust*shortest**path*problem. ... We introduce a new*lower**bound*for*the*optimal value of*the*minmax regret problem. ... To compute*the**lower**bound*we have to do*one**shortest**path*computation (to find*the*value of*the*mid point*path*) as well as*one*run of Suurballe's algorithm. ...##
###
A lower bound on the expected optimal value of certain random linear programs and application to shortest paths in Directed Acyclic Graphs and reliability

2016
*
Statistics and Probability Letters
*

*The*paper studies

*the*expectation of

*the*inspection time in complex aging systems, i.e.

*the*length of

*the*

*shortest*

*path*in a Directed Acyclic Graph, with random costs

*on*egdes. ... We give a

*lower*

*bound*for this expectation. ...

*The*goal of this paper is to propose a

*lower*

*bound*

*on*

*the*expected length of

*the*

*shortest*

*path*.

*The*paper is organized as follows. ...

##
###
Stochastic Shortest Paths and Risk Measures
[article]

2014
*
arXiv
*
pre-print

*One*of

*the*key elements in these algorithms is

*the*use of stochastic

*lower*

*bounds*that allow to discard partial solutions. ... Good stochastic

*lower*

*bounds*are provided by

*the*so-called Stochastic Ontime Arrival Problem. ... Stochastic

*lower*

*bounds*and

*On*Time Arrival 4.1. Stochastic

*lower*

*bounds*. ...

##
###
First-Passage Percolation on a Width-2 Strip and the Path Cost in a VCG Auction
[chapter]

2006
*
Lecture Notes in Computer Science
*

We rely

doi:10.1007/11944874_10
fatcat:2flki45fnvcslg2riovbz35z24
*on*no special properties of*the*uniform*distribution*;*the*same methods could be applied to any well-behaved,*bounded**distribution*. ... This paper studies*the*time constant for first-passage percolation and*the*Vickery-Clarke-Groves (VCG) payment for*the**shortest**path**on*a width-2 strip with random edge costs. ... necessarily a*lower**bound**on*∆. ...##
###
On the Communication Complexity of Distributed Name-Independent Routing Schemes
[chapter]

2013
*
Lecture Notes in Computer Science
*

This factor is provable thanks to a new

doi:10.1007/978-3-642-41527-2_29
fatcat:ytut6bndxfecxhprk3pn4zl4ry
*lower**bound*of independent interest. ... routing scheme*on**the*same family of networks. ...*One*may also think that*the*second*lower**bound*is again folklore since clearly a*shortest*-*path*routing scheme must send at least*one*message*on*each edge. ...##
###
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. ...
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