scholarly journals An all-pairs shortest path algorithm for bipartite graphs

2013 ◽  
Vol 3 (4) ◽  
Author(s):  
Svetlana Torgasin ◽  
Karl-Heinz Zimmermann
Keyword(s):  
Shortest Path ◽  
Time Complexity ◽  
Shortest Paths ◽  
Distance Matrix ◽  
Bipartite Graphs ◽  
Matrix Product ◽  
Complex Structures ◽  
Shortest Path Algorithm ◽  
Order Of Magnitude ◽  
All Pairs Shortest Path

AbstractBipartite graphs are widely used for modeling of complex structures in biology, engineering, and computer science. The search for shortest paths in such structures is a highly demanded procedure that requires optimization. This paper presents a variant of the all-pairs shortest path algorithm for bipartite graphs. The method is based on the distance matrix product and improves the general algorithm by exploiting the graph topology. The space complexity is reduced by a factor of at least four and the time complexity decreased by almost an order of magnitude when compared with the basic APSP algorithm.

Maintaining Constrained Path Problem for Directed Acyclic Graphs

2021 ◽  
Vol 21 (03) ◽  
Author(s):  
Chenying Hao ◽  
Shurong Zhang ◽  
Weihua Yang
Keyword(s):  
Shortest Path ◽  
Time Complexity ◽  
Directed Acyclic Graph ◽  
Shortest Paths ◽  
Directed Acyclic Graphs ◽  
Shortest Path Algorithm ◽  
Acyclic Graphs ◽  
Main Technique ◽  
Number Formula ◽  
The One

In order to restore the faulty path in network more effectively, we propose the maintaining constrained path problem. Give a directed acyclic graph (DAG) [Formula: see text] with some faulty edges, where [Formula: see text], [Formula: see text]. For any positive number [Formula: see text], we give effective maintain algorithm for finding and maintaining the path between source vertex [Formula: see text] and destination [Formula: see text] with length at most [Formula: see text]. In this paper, we consider the parameters [Formula: see text] and [Formula: see text] which are used to measure the numbers of edges and vertices which are influenced by faulty edges, respectively. The main technique of this paper is to define and solve a subproblem called the one to set constrained path problem (OSCPP) which has not been addressed before. On the DAG, compared with the dynamic shortest path algorithm with time complexity [Formula: see text] [16] and the shortest path algorithm with time complexity [Formula: see text] [18], based on the algorithm for OSCPP, we develop a maintaining constrained path algorithm and improve the time complexity to [Formula: see text] in the case that all shortest paths from each vertex [Formula: see text] to [Formula: see text] have been given.

Finding the Shortest Path on a Polyhedral Surface and Its Application to Quality Assurance of Electric Components

2004 ◽  
Vol 126 (6) ◽  
pp. 1017-1026 ◽  
Author(s):  
Masaru Kageura ◽  
Kenji Shimada
Keyword(s):  
Product Design ◽  
Shortest Path ◽  
Shortest Paths ◽  
Computational Cost ◽  
Computational Method ◽  
Polyhedral Surface ◽  
Global Optimality ◽  
Shortest Path Algorithm ◽  
Suzuki Method ◽  
Polyhedral Surfaces

This paper presents a computational method for finding the shortest path along polyhedral surfaces. This method is useful for verifying that there is a sufficient distance between two electrical components to prevent the occurrence of a spark between them in product design. We propose an extended algorithm based on the Kanai-Suzuki method, which finds an approximate shortest path by reducing the problem to searching the shortest path on the discrete weighted graph that corresponds to a polyhedral surface. The accuracy of the solution obtained by the Kanai-Suzuki method is occasionally insufficient for our requirements in product design. To achieve higher accuracy without increasing the computational cost drastically, we extend the algorithm by adopting two additional methods: “geometrical improvement” and the “K shortest path algorithm.” Geometrical improvement improves the local optimality by using the geometrical information around a path obtained by the graph method. The K shortest path algorithm, on the other hand, improves the global optimality by finding multiple initial paths for searching the shortest path. For some representative polyhedral surfaces we performed numerical experiments and demonstrated the effectiveness of the proposed method by comparing the shortest paths obtained by the Chen-Han exact method and the Kanai-Suzuki approximate method with the ones obtained by our method.

Improvement A* Algorithm Based on Dynamic Consistency Assumption

2011 ◽  
Vol 97-98 ◽  
pp. 883-887
Author(s):  
Liang Zou ◽  
Zi Zhang ◽  
Ling Xiang Zhu
Keyword(s):  
Lower Bound ◽  
Shortest Path ◽  
Dynamic Networks ◽  
Shortest Paths ◽  
Dynamic Consistency ◽  
Destination Node ◽  
Shortest Path Algorithm ◽  
A Algorithm ◽  
Dynamic Form

Efficient dynamic shortest path algorithm in static networks plays an important role in ITS. To solve this problem, this paper brings forward the dynamic form of Consistency Assumption and Dynamic A* algorithm (A* algorithm based on dynamic lower bound, DA* algorithm) based on dynamic lower bound. DA* algorithm and the dynamic form of Consistency Assumption are described in detail. It is proved that DA* algorithm can solve one origin node to one destination node shortest paths problem in dynamic networks, if DA* algorithm’s dynamic lower bound satisfies the dynamic form of Consistency Assumption.

scholarly journals Data Security and Shortest Path Finding in IOT

2019 ◽  
pp. 551-557
Author(s):  
W. Winfredruby ◽  
S Sivagurunathan
Keyword(s):  
Shortest Path ◽  
Humidity Sensor ◽  
Shortest Paths ◽  
Data Access ◽  
Destination Node ◽  
Network Congestion ◽  
Shortest Path Algorithm ◽  
Sensor Applications ◽  
Encryption And Decryption ◽  
The Internet Of Things

Nowadays with the rapid growth of the smart city and the internet of things applications are difficult to connect the data access center, to meet service requirements with low latency and high quality while sending and receiving data access requests. At the same time, lower security performance occurred. In temperature and humidity sensor applications we approach a cryptography technique to protect data. It is an ASCII values-based technique which uses some numerical calculation to perform encryption and decryption. Then the use of the shortest path algorithm we find an entire possible path using current node detail and the destination node is sent by the source node to the neighbourhood nodes. Neighbourhood node receives the detail and checks the destination node. In case, the neighbourhood node is not the destination, it appends its detail along with the received details and sends to its neighbourhood nodes and the process continues till reaching the destination. By calculating the link delay between the two nodes. We can find the delay time taken from source to destination. At last we display the entire possible shortest paths and secure data. It is useful when network congestion occurs. In this paper, we also overcome this problem.

Research and development of Johnson's algorithm parallel schemes in GPGPU technology

2016 ◽  
pp. 105-112
Author(s):  
S.D. Pogorilyy ◽  
◽  
M.S. Slynko ◽  
Keyword(s):  
Experimental Study ◽  
Research And Development ◽  
Shortest Path ◽  
Shortest Path Algorithm ◽  
Suggested Approach ◽  
Nvidia Cuda ◽  
Weighted Directed Graph ◽  
Improved Performance ◽  
Systems Of Algorithmic Algebras ◽  
All Pairs Shortest Path

Johnson’s all pairs shortest path algorithm application in an edge weighted, directed graph is considered. Its formalization in terms of Glushkov’s modified systems of algorithmic algebras was made. The expediency of using GPGPU technology to accelerate the algorithm is proved. A number of schemas of parallel algorithm optimized for using in GPGPU were obtained. Suggested approach to the implementation of the schemes obtained using computing architecture NVIDIA CUDA. An experimental study of improved performance by using GPU for computations was made.

NC ALGORITHMS FOR THE SINGLE MOST VITAL EDGE PROBLEM WITH RESPECT TO ALL PAIRS SHORTEST PATHS

2000 ◽  
Vol 10 (01) ◽  
pp. 51-58 ◽  
Author(s):  
SVEN VENEMA ◽  
HONG SHEN ◽  
FRANCIS SURAWEERA
Keyword(s):  
Shortest Path ◽  
Shortest Paths ◽  
Sequential Algorithm ◽  
Single Edge ◽  
All Pairs Shortest Paths ◽  
Shortest Distance ◽  
Straightforward Solution ◽  
All Pairs Shortest Path ◽  
The Impact ◽  
Crcw Pram

For a weighted, undirected graph G=(V, E) where |V|=n and |E|=m, we examine the single most vital edge with respect to all-pairs shortest paths (APSP) under two different measurements. The first measurement considers only the impact of the removal of a single edge from the APSP on the shortest distance between each vertex pair. The second considers the total weight of all the edges which make up the APSP, that is, calculate the sum of the distance between each vertex pair after the deletion of any edge belonging to a shortest path. We give a sequential algorithm for this problem, and show how to obtain an NC algorithm running in O( log n) time using mn2 processors and O(mn2) space on the MINIMUM CRCW PRAM. Given the shortest distance between each pair of vertices u and v, the diameter of the graph is defined as the longest of these distances. The Most vital edge with respect to the diameter is the edge lying on such a u–v shortest path which when removed causes the greatest increase in the diameter. We show how to modify the above algorithm to solve this problem using the same time and number of processors. Both algorithms compare favourably with the straightforward solution which simply recalculates the all pairs shortest path information.

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