Complete digraphs of various sizes with the number of relaxations of algorithms divided by n 3 .

Complete digraphs of various sizes with the number of relaxations of algorithms divided by n 3 .

Contexts in source publication

Context 1
... results of the first experiment, in which R F W = n 3 since digraphs are complete, are presented in Figure 1. To relate the theoretical upper bound of O(n 2 lg 2 n) of the Tree algorithm and the experimental results, we added also the plot of the function 60 n 2 lg 2 n n 3 . ...
Context 2
... chose the constant 60 so that the plots of the Tree algorithm and the added function start at the same initial point, namely at 2 8 vertices. The results of the second experiment for = 1024 vertices and sizes of the arc set varying between n 2 /10 and 8n 2 /10 are shown in Figure 2. In Figure 1 we see a significant reduction of relaxations which also implies the decrease of running time of the Tree and Hourglass algorithms. From the plot we can also see that the experimental results indicate that the theoretical upper bound of the Tree algorithm is asymptotic tight. ...

Similar publications

Article
Full-text available
ABSTRACT Maritime shipping is vital to worldwide commerce. Due to the high flow in ports throughout the world, the efficient allocation of vessels in berths has become a problem. A new mathematical model and several algorithms are proposed in this paper to planning the allocation of the vessels in berths and the allocation of resources to the servi...
Article
Full-text available
The paper focuses on the Enhanced Augmented Lagrangian method with sparse regularization for image deblurring. The method suggested by ALTERNATING LOW RANK AUGMENTED LAGRANGIAN WITH ITERATIVE A PRIOR is novel in the following ways. (i) Faster convergence leading to speeder execution through rank regulations (ii) using derivatives and low rank toget...
Article
Full-text available
Aiming at the problem of ORB feature matching algorithm extracting background pixels as feature points and matching wrong feature points in a complex background environment, an improved ORB algorithm based on adaptive threshold is proposed, and GMS algorithm is used to screen out mismatches in the feature matching stage. First, the algorithm calcul...
Article
Full-text available
In this paper, the flashlight (FL) algorithm, which is categorized as a heuristic method, has been suggested to determine the ultimate pit limit (UPL). In order to apply the suggested algorithm and other common algorithms, such as the dynamic programming, the Korobov, and the floating cone, and to validate the capability of the proposed method, the...

Citations

... Consequently, we are not solving n, where n is a number of nodes, unrelated SSSP problems, but one single all-pairs shortest path problem (APSP). The traditional algorithm solving this problem is a dynamic-programming centralized Floyd-Warshall algorithm ( [44,48]). Indeed, some attempts were made to make it parallel, and most of them applied techniques used in parallel matrix multiplication (cf. [49]). ...
Article
Full-text available
Indoor Air Quality monitoring is a major asset to improving quality of life and building management. Today, the evolution of embedded technologies allows the implementation of such monitoring on the edge of the network. However, several concerns need to be addressed related to data security and privacy, routing and sink placement optimization, protection from external monitoring, and distributed data mining. In this paper, we describe an integrated framework that features distributed storage, blockchain-based Role-based Access Control, onion routing, routing and sink placement optimization, and distributed data mining to answer these concerns. We describe the organization of our contribution and show its relevance with simulations and experiments over a set of use cases.
Article
    The Floyd‐Warshall algorithm is the most popular algorithm for determining the shortest paths between all vertex pairs in a graph. It is a very simple and an elegant algorithm. However, for graphs without any negative weighted edges, using Dijkstra's shortest path algorithm for every vertex as a source vertex to produce all‐pairs shortest paths works significantly better than the Floyd‐Warshall algorithm, especially for large graphs. Furthermore, for graphs with negative weighted edges, with no negative cycle, in general Johnson's algorithm also performs better than the Floyd‐Warshall algorithm for large graphs. Johnson's algorithm first transforms the graph into a non‐negative one by using the Bellman‐Ford algorithm, then applies the Dijkstra's algorithm to the transformed graph. Thus, mainly, the Floyd‐Warshall algorithm is quite inefficient, especially for large graphs. In this paper, we show a simple improvement on the Floyd‐Warshall algorithm that will increases its efficiency, especially for very sparse graphs (i.e., the number of its edges is less than the number of its vertices), so it can be used instead of more complicated alternatives. We also show that our approach is also very effective for denser disconnected graphs. Since the new algorithm modifies the original Floyd‐Warshall algorithm, it is mainly aimed for directed graphs without negative cycles. Most programmers prefer to implement the Floyd‐Warshall algorithm over more complicated but more efficient alternatives for solving all‐pairs shortest path problems. In this work, we show that without the addition of any complicated data structures, the performance of the Floyd‐Warshall algorithm can be improved very easily. Our practical approach works even better than its alternatives for large sparse graphs.
    Article
    Full-text available
    The basic goal of this research is to find the shortest path of a semidirected graph and apply it to the road network system. In the field of graph theory, networks are described as directed graphs, undirected graphs, or a combination of both. However, in the modern era of computing, several networks, such as social media networks, granular networks, and road transport networks, are not linked to any of the aforementioned network categories and in reality are a hybrid of networks with both directed and undirected interconnections. To better understand the notion of these types of networks, semidirected graphs have been developed to represent such networks. In a sem-idirect graph, both the directed and undirected edges concepts have been introduced together in a graph. In reality, it has been noted that for every node (source/destination) which is connected to another, some links/connections are directed-i.e., one-way-and some links/connections are undi-rected-i.e., two-way. Considering that there is no specific direction provided and that two nodes are connected, we have established the concept of an undirected edge as two-way connectivity since this provides for nodes in both ways. In this study, the road network system has been modelled using the concept of a semidirected graph, and the shortest path through it has been determined. For the purposes of illustration, we have used a real transportation road network in this case, and the computed results have been displayed.