scholarly journals DMGA: A Distributed Shortest Path Algorithm for Multistage Graph

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Huanqing Cui ◽  
Ruixue Liu ◽  
Shaohua Xu ◽  
Chuanai Zhou
Keyword(s):  
Shortest Path ◽  
Large Scale ◽  
Structural Characteristics ◽  
Shortest Paths ◽  
Dynamic Programming Algorithm ◽  
Special Kind ◽  
Graph Algorithm ◽  
Shortest Path Problem ◽  
Programming Algorithm ◽  
Classical Dynamic

The multistage graph problem is a special kind of single-source single-sink shortest path problem. It is difficult even impossible to solve the large-scale multistage graphs using a single machine with sequential algorithms. There are many distributed graph computing systems that can solve this problem, but they are often designed for general large-scale graphs, which do not consider the special characteristics of multistage graphs. This paper proposes DMGA (Distributed Multistage Graph Algorithm) to solve the shortest path problem according to the structural characteristics of multistage graphs. The algorithm first allocates the graph to a set of computing nodes to store the vertices of the same stage to the same computing node. Next, DMGA calculates the shortest paths between any pair of starting and ending vertices within a partition by the classical dynamic programming algorithm. Finally, the global shortest path is calculated by subresults exchanging between computing nodes in an iterative method. Our experiments show that the proposed algorithm can effectively reduce the time to solve the shortest path of multistage graphs.

scholarly journals A dynamic programming algorithm for solving the k-Color Shortest Path Problem

2020 ◽  
Author(s):  
Daniele Ferone ◽  
Paola Festa ◽  
Serena Fugaro ◽  
Tommaso Pastore
Keyword(s):  
Mathematical Model ◽  
Dynamic Programming ◽  
Branch And Bound ◽  
Shortest Path ◽  
Dynamic Programming Algorithm ◽  
Shortest Path Problem ◽  
Programming Algorithm ◽  
Colored Graph ◽  
Transmission Networks ◽  
The Mathematical Model

Abstract Several variants of the classical Constrained Shortest Path Problem have been presented in the literature so far. One of the most recent is the k-Color Shortest Path Problem ($$k$$ k -CSPP), that arises in the field of transmission networks design. The problem is formulated on a weighted edge-colored graph and the use of the colors as edge labels allows to take into account the matter of path reliability while optimizing its cost. In this work, we propose a dynamic programming algorithm and compare its performances with two solution approaches: a Branch and Bound technique proposed by the authors in their previous paper and the solution of the mathematical model obtained with CPLEX solver. The results gathered in the numerical validation evidenced how the dynamic programming algorithm vastly outperformed previous approaches.

scholarly journals Simulation-Based Electric Vehicle Sustainable Routing with Time-Dependent Stochastic Information

2020 ◽  
Vol 12 (6) ◽  
pp. 2464 ◽  
Author(s):  
Xinran Li ◽  
Haoxuan Kan ◽  
Xuedong Hua ◽  
Wei Wang
Keyword(s):  
Shortest Path ◽  
Dynamic Programming Algorithm ◽  
Shortest Path Problem ◽  
Time Dependent ◽  
Programming Algorithm ◽  
Search Problem ◽  
Simulation Based ◽  
Markov Decision ◽  
Improve Calculation ◽  
Charging Stations

We propose a routing method for electric vehicles that finds a route with minimal expected travel time in time-dependent stochastic networks. The method first estimates whether the vehicle can reach the destination with the current battery level and selects potential reasonable charging stations if needed. Then, the route-search problem is formulated as a shortest path problem with time-dependent stochastic disruptions, using a Markov decision process. The shortest path problem is solved by an approximate dynamic programming algorithm to improve calculation efficiency in complex networks. Several simulation cases and a scenario-based example are given to prove the validity of the method.

scholarly journals A Comprehensive Comparison of Label Setting Algorithm and Dynamic Programming Algorithm in Solving Shortest Path Problems

2021 ◽  
Vol 13 (5) ◽  
pp. 14
Author(s):  
Douglas Yenwon Kparib ◽  
John Awuah Addor ◽  
Anthony Joe Turkson
Keyword(s):  
Dynamic Programming ◽  
Shortest Path ◽  
Shortest Paths ◽  
Dynamic Programming Algorithm ◽  
Minimum Cost ◽  
Programming Algorithm ◽  
Shortest Path Problems ◽  
Comprehensive Comparison ◽  
Paper Label ◽  
Label Setting Algorithm

In this paper, Label Setting Algorithm and Dynamic Programming Algorithm had been critically examined in determining the shortest path from one source to a destination. Shortest path problems are for finding a path with minimum cost from one or more origin (s) to one or more destination(s) through a connected network. A network of ten (10) cities (nodes) was employed as a numerical example to compare the performance of the two algorithms. Both algorithms arrived at the optimal distance of 11 km, which corresponds to the paths 1→4→5→8→10 ,1→3→5→8→10 , 1→2→6→9→10  and  1→4→6→9→10 . Thus, the problem has multiple shortest paths. The computational results evince the outperformance of Dynamic Programming Algorithm, in terms of time efficiency, over the Label Setting Algorithm. Therefore, to save time, it is recommended to apply Dynamic Programming Algorithm to shortest paths and other applicable problems over the Label-Setting Algorithm.

Multidimensional Parallel Dynamic Programming Algorithm Based on Spark for Large-Scale Hydropower Systems

2020 ◽  
Vol 34 (11) ◽  
pp. 3427-3444 ◽  
Author(s):  
Yufei Ma ◽  
Ping-an Zhong ◽  
Bin Xu ◽  
Feilin Zhu ◽  
Yao Xiao ◽  
...  
Keyword(s):  
Dynamic Programming ◽  
Large Scale ◽  
Dynamic Programming Algorithm ◽  
Programming Algorithm

The shortest path problem on large-scale real-road networks

Networks ◽  
2006 ◽  
Vol 48 (4) ◽  
pp. 182-194 ◽  
Author(s):  
G.A. Klunder ◽  
H.N. Post
Keyword(s):  
Shortest Path ◽  
Large Scale ◽  
Road Networks ◽  
Shortest Path Problem

An Approximate Dynamic Programming Algorithm for Large-Scale Fleet Management: A Case Application

2009 ◽  
Vol 43 (2) ◽  
pp. 178-197 ◽  
Author(s):  
Hugo P. Simão ◽  
Jeff Day ◽  
Abraham P. George ◽  
Ted Gifford ◽  
John Nienow ◽  
...  
Keyword(s):  
Dynamic Programming ◽  
Large Scale ◽  
Approximate Dynamic Programming ◽  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Fleet Management ◽  
Case Application
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