scholarly journals Prograph Based Analysis of Single Source Shortest Path Problem with Few Distinct Positive Lengths

2011 ◽  
Vol 1 (4) ◽  
pp. 90-97
Author(s):  
B. Bhowmik ◽  
S. Nag Chowdhury
Keyword(s):  
Shortest Path ◽  
Directed Graphs ◽  
Algorithm Design ◽  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Single Source ◽  
Comparison Study ◽  
Design Technique ◽  
Shortest Path Problems ◽  
Finite Directed Graphs

In this paper we propose an experimental study model S3P2 of a fast fully dynamic programming algorithm design technique in finite directed graphs with few distinct nonnegative real edge weights. The Bellman-Ford’s approach for shortest path problems has come out in various implementations. In this paper the approach once again is re-investigated with adjacency matrix selection in associate least running time. The model tests proposed algorithm against arbitrarily but positive valued weighted digraphs introducing notion of  Prograph that speeds up finding the shortest path over previous implementations. Our experiments have established abstract results with the intention that the proposed algorithm can consistently dominate other existing algorithms for Single Source Shortest Path Problems. A comparison study is also shown among Dijkstra’s algorithm, Bellman-Ford algorithm, and our algorithm.

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.

scholarly journals Adding Edges for Maximizing Weighted Reachability

Algorithms ◽  
2020 ◽  
Vol 13 (3) ◽  
pp. 68 ◽  
Author(s):  
Federico Corò ◽  
Gianlorenzo D'Angelo ◽  
Cristina M. Pinotti
Keyword(s):  
Polynomial Time ◽  
Greedy Algorithms ◽  
Dynamic Programming Algorithm ◽  
Directed Acyclic Graphs ◽  
Constant Factor ◽  
Programming Algorithm ◽  
Single Source ◽  
Graph Augmentation ◽  
Set Size ◽  
Acyclic Graphs

In this paper, we consider the problem of improving the reachability of a graph. We approach the problem from a graph augmentation perspective, in which a limited set size of edges is added to the graph to increase the overall number of reachable nodes. We call this new problem the Maximum Connectivity Improvement (MCI) problem. We first show that, for the purpose of solve solving MCI, we can focus on Directed Acyclic Graphs (DAG) only. We show that approximating the MCI problem on DAG to within any constant factor greater than 1 − 1 / e is NP -hard even if we restrict to graphs with a single source or a single sink, and the problem remains NP -complete if we further restrict to unitary weights. Finally, this paper presents a dynamic programming algorithm for the MCI problem on trees with a single source that produces optimal solutions in polynomial time. Then, we propose two polynomial-time greedy algorithms that guarantee ( 1 − 1 / e ) -approximation ratio on DAGs with a single source, a single sink or two sources.

scholarly journals An efficient approach for solving Travelling Sales Man Problem

2021 ◽  
Vol 9 (8) ◽  
pp. 2793--2798
Author(s):  
Tirumalasetti Guna Sekhar
Keyword(s):  
Urban Communities ◽  
Shortest Path ◽  
Urban Areas ◽  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Dijkstra Algorithm ◽  
A Algorithm ◽  
Fundamental Goal ◽  
Time And Space Complexity ◽  
The City

Abstract: Global Position System (GPS) application is quite possibly the most valuable instrument in transportation the executives nowadays. The Roadway transportation is an significant function of GPS. To track down the briefest courses to a spot is the key issue of organization investigation. To address this issue, we have numerous calculations and procedures like Dijkstra algorithm, Ant Colony Optimization, Bellman Portage Algorithm, Floyd-Warshall algorithm, Genetic Algorithm, A* Algorithm furthermore, numerous others. In this paper our fundamental goal is to assess the brute force algorithm and the dynamic programming algorithm in settling the Shortest path issue (The travelling salesman issue). The paper will be finished up by giving the results of time and space complexity of these algorithms. To help a salesman visit every one of the urban communities in the rundown (giving the area of urban areas as the information) and he knows the area of the multitude of urban communities and track down the shortest path with the end goal that he visits every one of the urban areas just a single time and gets back to the city where he begun. The distance (cost) and the relating way ought to be shown as yield.

Time-Dependent Shortest Path Problems with Penalties and Limits on Waiting

2020 ◽  
Author(s):  
Edward He ◽  
Natashia Boland ◽  
George Nemhauser ◽  
Martin Savelsbergh
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Shortest Path ◽  
Complexity Analysis ◽  
Fundamental Problem ◽  
Algorithm Design ◽  
Weather Conditions ◽  
Time Dependent ◽  
Shortest Path Problems ◽  
The Right

Waiting at the right location at the right time can be critically important in certain variants of time-dependent shortest path problems. We investigate the computational complexity of time-dependent shortest path problems in which there is either a penalty on waiting or a limit on the total time spent waiting at a given subset of the nodes. We show that some cases are nondeterministic polynomial-time hard, and others can be solved in polynomial time, depending on the choice of the subset of nodes, on whether waiting is penalized or constrained, and on the magnitude of the penalty/waiting limit parameter. Summary of Contributions: This paper addresses simple yet relevant extensions of a fundamental problem in Operations Research: the Shortest Path Problem (SPP). It considers time-dependent variants of SPP, which can account for changing traffic and/or weather conditions. The first variant that is tackled allows for waiting at certain nodes but at a cost. The second variant instead places a limit on the total waiting. Both variants have applications in transportation, e.g., when it is possible to wait at certain locations if the benefits outweigh the costs. The paper investigates these problems using complexity analysis and algorithm design, both tools from the field of computing. Different cases are considered depending on which of the nodes contribute to the waiting cost or waiting limit (all nodes, all nodes except the origin, a subset of nodes…). The computational complexity of all cases is determined, providing complexity proofs for the variants that are NP-Hard and polynomial time algorithms for the variants that are in P.

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 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.

REACHABILITY ANALYSIS FOR UNCERTAIN SSPs

2007 ◽  
Vol 16 (04) ◽  
pp. 725-749
Author(s):  
OLIVIER BUFFET
Keyword(s):  
Transition Probability ◽  
Dynamic Programming Algorithm ◽  
Complex Case ◽  
Programming Algorithm ◽  
Time Dynamic ◽  
Goal State ◽  
Stochastic Shortest Path ◽  
Shortest Path Problems ◽  
Complete State ◽  
Stochastic Shortest Path Problems

Stochastic Shortest Path problems (SSPs) can be efficiently dealt with by the Real-Time Dynamic Programming algorithm (RTDP). Yet, RTDP requires that a goal state is always reachable. This article presents an algorithm checking for goal reachability, especially in the complex case of an uncertain SSP where only a possible interval is known for each transition probability. This gives an analysis method for determining if SSP algorithms such as RTDP are applicable, even if the exact model is not known. As this is a time-consuming algorithm, we also present a simple process that often speeds it up dramatically. Yet, the main improvement still needed is to turn to a symbolic analysis in order to avoid a complete state-space enumeration.

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.

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