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

Axel Parmentier
2017 arXiv   pre-print
Recent improvements of these enumeration algorithms rely 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.  ... 
arXiv:1504.07880v2 fatcat:4up4vrxudfa3fmgxx6gzhgkd24

Computing Shortest Paths Using A*, Landmarks, and Polygon Inequalities (Abstract) [article]

Newton Campbell Jr
2016 arXiv   pre-print
This heuristic's benefits are permitted by a new approach for computing 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.  ... 
arXiv:1603.01607v1 fatcat:izoxkc3ovbajrkdash3vhpln2a

Distributed Processing of k Shortest Path Queries over Dynamic Road Networks [article]

Ziqiang Yu, Xiaohui Yu, Nick Koudas, Yang Liu, Yifan Li, Yueting Chen, Dingyu Yang
2022 arXiv   pre-print
However, most existing approaches are designed to identify KSPs 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  ... 
arXiv:2004.02580v3 fatcat:czasqu4ngbhpdi2fh23ysl2dcm

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

David R. Karger, Daphne Koller, Steven J. Phillips
1993 SIAM journal on computing (Print)  
Finally, we prove an (mn) 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.  ... 
doi:10.1137/0222071 fatcat:wn3ogqqw4vc5bfsgcjeise6lqy

Estimation of Shortest Path Covariance Matrices [article]

Raj Kumar Maity, Cameron Musco
2020 arXiv   pre-print
In particular, we focus 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  ... 
arXiv:2011.09986v1 fatcat:2mortzq7hraerhe36jkgdkfade

Brief Announcement: Near Optimal Bounds for Replacement Paths and Related Problems in the CONGEST Model

Vignesh Manoharan, Vijaya Ramachandran
2022 Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing  
We present round complexity results in 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.  ... 
doi:10.1145/3519270.3538473 fatcat:s3b2sphdp5ehvocrsuykmaoqyi

A nearly optimal distributed algorithm for computing the weighted girth

Qiang-Sheng Hua, Lixiang Qian, Dongxiao Yu, Xuanhua Shi, Hai Jin
2021 Science China Information Sciences  
Instead of computing all pairs 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] .  ... 
doi:10.1007/s11432-020-2931-x fatcat:eg4vwzqa75axrbzevgoz356yzm

A Simple Ant Colony Optimizer for Stochastic Shortest Path Problems

Dirk Sudholt, Christian Thyssen
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  ... 
doi:10.1007/s00453-011-9606-2 fatcat:dkzgcvawszcytbnz7xs4oenrcy

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

Stephane Chretien, Franck Corset
2016 arXiv   pre-print
Under reasonable assumptions, this problem is reduced to studying 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.  ... 
arXiv:1504.00865v2 fatcat:7skh7j4l6zhdzg66y3pmpq6fii

A new bound for the midpoint solution in minmax regret optimization with an application to the robust shortest path problem

André B. Chassein, Marc Goerigk
2015 European Journal of Operational Research  
To illustrate 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.  ... 
doi:10.1016/j.ejor.2015.02.023 fatcat:mn4q6exagzghzeh6v45lzrs4em

A lower bound on the expected optimal value of certain random linear programs and application to shortest paths in Directed Acyclic Graphs and reliability

Stéphane Chrétien, Franck Corset
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.  ... 
doi:10.1016/j.spl.2016.06.001 fatcat:4c4o5p4llbb6negxoqjoo3snfi

Stochastic Shortest Paths and Risk Measures [article]

Axel Parmentier, Frédéric Meunier
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.  ... 
arXiv:1408.0272v2 fatcat:4maqvf5v4bayze4rzoa5o7c2t4

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

Abraham Flaxman, David Gamarnik, Gregory B. Sorkin
2006 Lecture Notes in Computer Science  
We rely 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 ∆.  ... 
doi:10.1007/11944874_10 fatcat:2flki45fnvcslg2riovbz35z24

On the Communication Complexity of Distributed Name-Independent Routing Schemes [chapter]

Cyril Gavoille, Christian Glacet, Nicolas Hanusse, David Ilcinkas
2013 Lecture Notes in Computer Science  
This factor is provable thanks to a new 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.  ... 
doi:10.1007/978-3-642-41527-2_29 fatcat:ytut6bndxfecxhprk3pn4zl4ry

Lagrangian Relaxation for the Multiple Constrained Robust Shortest Path Problem

Yiyong Pan
2019 Mathematical Problems in Engineering  
Nonlinear optimization model is developed to model constrained robust 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.  ... 
doi:10.1155/2019/3987278 fatcat:iz4yjehrn5e2jhxdhr7fi6tl5i
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