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A Lower Bound for the Shortest Path Problem

Ketan Mulmuley, Pradyut Shah
2001 Journal of computer and system sciences (Print)  
This shows that 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.  ... 
doi:10.1006/jcss.2001.1766 fatcat:lmh77vnl7fadzfbayiq7c3z3xa

A lower bound for the shortest path problem

K. Mulmuley, P. Shah
Proceedings 15th Annual IEEE Conference on Computational Complexity  
This shows that 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.  ... 
doi:10.1109/ccc.2000.856731 dblp:conf/coco/MulmuleyS00 fatcat:e44jvkuykve2tmb2ugjqn34qpy

On the difficulty of some shortest path problems

John Hershberger, Subhash Suri, Amit Bhosle
2007 ACM Transactions on Algorithms  
We prove super-linear 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] .  ... 
doi:10.1145/1219944.1219951 fatcat:ernhz2cdmjhqnim5ht7ubbblme

On the Difficulty of Some Shortest Path Problems [chapter]

John Hershberger, Subhash Suri, Amit Bhosle
2003 Lecture Notes in Computer Science  
We prove super-linear 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] .  ... 
doi:10.1007/3-540-36494-3_31 fatcat:tceizql3cfeadfwcb6aiftuolu

On the difficulty of some shortest path problems

John Hershberger, Subhash Suri, Amit Bhosle
2007 ACM Transactions on Algorithms  
We prove super-linear 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] .  ... 
doi:10.1145/1186810.1186815 fatcat:4msbqoswtzhk7nv7qdbhkntkfu

Adaptations of the A* algorithm for the computation of fastest paths in deterministic discrete-time dynamic networks

I. Chabini, Shan Lan
2002 IEEE transactions on intelligent transportation systems (Print)  
These 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.  ... 
doi:10.1109/6979.994796 fatcat:rcnja5ga55fephcdrhasksyxya

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

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

Axel Parmentier
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.  ... 
arXiv:1504.07880v2 fatcat:4up4vrxudfa3fmgxx6gzhgkd24

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

Running time analysis of Ant Colony Optimization for shortest path problems

Dirk Sudholt, Christian Thyssen
2012 Journal of Discrete Algorithms  
We present 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  ... 
doi:10.1016/j.jda.2011.06.002 fatcat:kia3okeal5d2vfqm3vunpxtske

On the Quadratic Shortest Path Problem [chapter]

Borzou Rostami, Federico Malucelli, Davide Frey, Christoph Buchheim
2015 Lecture Notes in Computer Science  
In this paper we model these situations as 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 .  ... 
doi:10.1007/978-3-319-20086-6_29 fatcat:e3e56wgofjcpbel42p4ntx52i4

Fast Robust Shortest Path Computations

Christoph Hansknecht, Alexander Richter, Sebastian Stiller, Michael Wagner
2018 Algorithmic Approaches for Transportation Modeling, Optimization, and Systems  
This methods generalizes to binary linear robust 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.  ... 
doi:10.4230/oasics.atmos.2018.5 dblp:conf/atmos/HansknechtRS18 fatcat:6k52ynz7gjhhjpvwagdgw3b7ny

A generalized permanent label setting algorithm for the shortest path between specified nodes

George L Nemhauser
1972 Journal of Mathematical Analysis and Applications  
ACKNOWLEDGIVIENT I IvYant to thank Guy de Ghellinck 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).  ... 
doi:10.1016/0022-247x(72)90091-1 fatcat:534zjw2ru5acnit65372evxsti

Finding All Hops Shortest Paths

G. Cheng, N. Ansari
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.  ... 
doi:10.1109/lcomm.2004.823365 fatcat:l5feb5fb6jabbhlrhjgycyapmy

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

Christian Horoba, Dirk Sudholt
2009 Lecture Notes in Computer Science  
We analyze 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.  ... 
doi:10.1007/978-3-642-03751-1_6 fatcat:ljzdzmeq7jefrfinfa4haifdwy
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