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.

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.

scholarly journals Potential Outcome and Directed Acyclic Graph Approaches to Causality: Relevance for Empirical Practice in Economics

2020 ◽  
Vol 58 (4) ◽  
pp. 1129-1179
Author(s):  
Guido W. Imbens
Keyword(s):  
Directed Acyclic Graph ◽  
Empirical Work ◽  
Directed Acyclic Graphs ◽  
Potential Outcome ◽  
Acyclic Graph ◽  
Acyclic Graphs ◽  
Outcome Framework ◽  
Outcome Perspective

In this essay I discuss potential outcome and graphical approaches to causality, and their relevance for empirical work in economics. I review some of the work on directed acyclic graphs, including the recent The Book of Why (Pearl and Mackenzie 2018). I also discuss the potential outcome framework developed by Rubin and coauthors (e.g., Rubin 2006), building on work by Neyman (1990 [1923]). I then discuss the relative merits of these approaches for empirical work in economics, focusing on the questions each framework answers well, and why much of the the work in economics is closer in spirit to the potential outcome perspective. (JEL C31, C36, I26)

MINIMIZATION OF PLANAR DIRECTED ACYCLIC GRAPH ALGEBRAS

2013 ◽  
Vol 24 (04) ◽  
pp. 519-531
Author(s):  
ANTONIOS KALAMPAKAS ◽  
OLYMPIA LOUSCOU-BOZAPALIDOU
Keyword(s):  
Directed Acyclic Graph ◽  
Directed Acyclic Graphs ◽  
Graph Algebras ◽  
Minimization Method ◽  
Nondeterministic Automaton ◽  
Acyclic Graph ◽  
Acyclic Graphs

We introduce planar directed acyclic graph algebras and present an explicit minimization method. The minimal simulation of a nondeterministic automaton on planar directed acyclic graphs is constructed.

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.

scholarly journals Phasertng: directed acyclic graphs for crystallographic phasing

2021 ◽  
Vol 77 (1) ◽  
pp. 1-10
Author(s):  
Airlie J. McCoy ◽  
Duncan H. Stockwell ◽  
Massimo D. Sammito ◽  
Robert D. Oeffner ◽  
Kaushik S. Hatti ◽  
...  
Keyword(s):  
Directed Acyclic Graph ◽  
Directed Acyclic Graphs ◽  
Molecular Replacement ◽  
Molecular Fragments ◽  
Graph Data ◽  
Acyclic Graphs ◽  
Structure Solution ◽  
Experimental Phasing ◽  
Graph Management ◽  
Extract Phase

Crystallographic phasing strategies increasingly require the exploration and ranking of many hypotheses about the number, types and positions of atoms, molecules and/or molecular fragments in the unit cell, each with only a small chance of being correct. Accelerating this move has been improvements in phasing methods, which are now able to extract phase information from the placement of very small fragments of structure, from weak experimental phasing signal or from combinations of molecular replacement and experimental phasing information. Describing phasing in terms of a directed acyclic graph allows graph-management software to track and manage the path to structure solution. The crystallographic software supporting the graph data structure must be strictly modular so that nodes in the graph are efficiently generated by the encapsulated functionality. To this end, the development of new software, Phasertng, which uses directed acyclic graphs natively for input/output, has been initiated. In Phasertng, the codebase of Phaser has been rebuilt, with an emphasis on modularity, on scripting, on speed and on continuing algorithm development. As a first application of phasertng, its advantages are demonstrated in the context of phasertng.xtricorder, a tool to analyse and triage merged data in preparation for molecular replacement or experimental phasing. The description of the phasing strategy with directed acyclic graphs is a generalization that extends beyond the functionality of Phasertng, as it can incorporate results from bioinformatics and other crystallographic tools, and will facilitate multifaceted search strategies, dynamic ranking of alternative search pathways and the exploitation of machine learning to further improve phasing strategies.

scholarly journals Task Scheduling in Heterogeneous Multiprocessor Environments – An Efficient ACO-Based Approach

2018 ◽  
Vol 10 (1) ◽  
pp. 320 ◽  
Author(s):  
Nekiesha Edward ◽  
Jeffrey Elcock
Keyword(s):  
Task Scheduling ◽  
Heterogeneous Computing ◽  
Optimization Technique ◽  
Shortest Paths ◽  
Directed Acyclic Graphs ◽  
Food Sources ◽  
Scheduling Problem ◽  
Ant Colonies ◽  
Acyclic Graphs ◽  
Critical Issues

In heterogeneous computing environments, finding optimized solutions continues to be one of the most important and yet, very challenging problems. Task scheduling in such environments is NP-hard, so efficient mapping of tasks to the processors remains one of the most critical issues to be tackled. For several types of applications, the task scheduling problem is crucial, and across the literature, a number of algorithms with several different approaches have been proposed. One such effective approach is known as Ant Colony Optimization (ACO). This popular optimization technique is inspired by the capabilities of ant colonies to find the shortest paths between their nests and food sources. Consequently, we propose an ACO-based algorithm, called rACS, as a solution to the task scheduling problem. Our algorithm utilizes pheromone and a priority-based heuristic, known as the upward rank value, as well as an insertion-based policy and a pheromone aging mechanism to guide the ants to high quality solutions. To evaluate the performance of our algorithm, we compared our algorithm with the ACS algorithm and the ACO-TMS algorithm using randomly generated directed acyclic graphs (DAGs). The simulation results indicated that our algorithm experienced comparable or even better performance, than the selected algorithms.

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