Approximately Counting Approximately-Shortest Paths in Directed Acyclic Graphs

2014 ◽  
Vol 58 (1) ◽  
pp. 45-59 ◽  
Author(s):  
Matúš Mihalák ◽  
Rastislav Šrámek ◽  
Peter Widmayer
Keyword(s):  
Shortest Paths ◽  
Directed Acyclic Graphs ◽  
Acyclic Graphs

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 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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