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A Lower Bound for the Shortest Path Problem
2001
Journal of computer and system sciences (Print)
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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
Proceedings 15th Annual IEEE Conference on Computational Complexity
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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
2007
ACM Transactions on Algorithms
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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]
2003
Lecture Notes in Computer Science
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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
2007
ACM Transactions on Algorithms
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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
2002
IEEE transactions on intelligent transportation systems (Print)
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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
2019
Mathematical Problems in Engineering
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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]
2017
arXiv
pre-print
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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
1993
SIAM journal on computing (Print)
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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
2012
Journal of Discrete Algorithms
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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]
2015
Lecture Notes in Computer Science
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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
2018
Algorithmic Approaches for Transportation Modeling, Optimization, and Systems
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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
1972
Journal of Mathematical Analysis and Applications
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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
2004
IEEE Communications Letters
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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]
2009
Lecture Notes in Computer Science
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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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