A generalization of Dijkstra's shortest path algorithm with applications to VLSI routing

AbstractWe generalize Dijkstra's algorithm for finding shortest paths in digraphs with non-negative integral edge lengths. Instead of labeling individual vertices we label subgraphs which partition the given graph. We can achieve much better running times if the number of involved subgraphs is small compared to the order of the original graph and the shortest path problems restricted to these subgraphs is computationally easy.As an application we consider the VLSI routing problem, where we need to find millions of shortest paths in partial grid graphs with billions of vertices. Here, our algorithm can be applied twice, once in a coarse abstraction (where the labeled subgraphs are rectangles), and once in a detailed model (where the labeled subgraphs are intervals). Using the result of the first algorithm to speed up the second one via goal-oriented techniques leads to considerably reduced running time. We illustrate this with a state-of-the-art routing tool on leading-edge industrial chips

Shortest Route at Dynamic Location with Node Combination-Dijkstra Algorithm

Online transportation has become a basic requirement of the general public in support of all activities to go to work, school or vacation to the sights. Public transportation services compete to provide the best service so that consumers feel comfortable using the services offered, so that all activities are noticed, one of them is the search for the shortest route in picking the buyer or delivering to the destination. Node Combination method can minimize memory usage and this methode is more optimal when compared to A* and Ant Colony in the shortest route search like Dijkstra algorithm, but can't store the history node that has been passed. Therefore, using node combination algorithm is very good in searching the shortest distance is not the shortest route. This paper is structured to modify the node combination algorithm to solve the problem of finding the shortest route at the dynamic location obtained from the transport fleet by displaying the nodes that have the shortest distance and will be implemented in the geographic information system in the form of map to facilitate the use of the system

Shortest Path Trajectory System Based on Dijkstra Algorithm

In the master project, the researcher discussed the shortest path solution to a single source problem based on Dijkstra algorithm as resolving the basic concepts. Everybody can travel by different routes to reach a different destination point. This can be time consuming if they do not travel trough the best route. This project aims to determine locations of the node that reflect all the items in the list, build the route by connecting nodes and evaluate the proposed algorithm for the single source shortest path problem. This project includes the modification of main algorithm which has been implemented in the prototype development. This study discussed the emphasis on the single source shortest path at the location of specific studies. The study will produce a decision-makers prototype

Path Planning Based on Fuzzy Decision Trees and Potential Field

The fuzzy logic algorithm is an artificial intelligence algorithm that uses mathematical logic to solve to by the data value inputs which are not precise in order to reach an accurate conclusion. In this work, Fuzzy decision tree (FDT) has been designed to solve the path planning problem by considering all available information and make the most appropriate decision given by the inputs. The FDT is often used to make a path planning decision in graph theory. It has been applied in the previous researches in the field of robotics, but it still shows drawbacks in that the robot will stop at the local minima and is not able to find the shortest path. Hence, this paper combines the FDT algorithm with the potential field algorithm. The potential field algorithm provides weight to the FDT algorithm which enables the robot to successfully avoid the local minima and find the shortest path

Rancang Bangun Transportasi Logistik Kakao Agroindustri Coklat Kabupaten Pidie Jaya Provinsi Aceh

Factual problems of the cocoa bean agroindustry at Pidie Jaya District, Aceh Province were large distances between farmers and processor, thus determining the shortest part route, backhaul location and quality risk becomes critically to the assess. The objective this research are to determine shortest route based on the location of suppliers, back location, and risk quality recommendations. Requirement of shortest part route solved by Algorithm Djisktra, Backhaul location with MPE and Risk management quality by Multi Expert Multi Criteria Decision Making, aggregation criteria with OWA. The result of the study shows that the shortest distance suppliers Aceh Timur District was 282km, Aceh Utara District 116km, Bireuen District 57km, Pidie District 24km and Aceh Tenggara District 391km. Backhaul location sat Aceh Tengah District with a value of MPE(6533). Alternative of quality risk management were direct fermentation, improvement of transport facilities and container with a high rating criteria, thus the agroindustry has to focus on this dimension

Solving Traveling Salesman Problem With a non-complete Graph

One of the simplest, but still NP-hard, routing problems is the Traveling Salesman Problem (TSP). In the TSP, one is given a set of cities and a way of measuring the distance between cities. One has to find the shortest tour that visits all cities exactly once and returns back to the starting city. In state-of-the-art algorithms, they all assume that a complete graph is given as an input. However, for very large graphs, generating all edges in a complete graph, which corresponds to finding shortest paths for all city pairs, could be time-consuming. This is definitely a major obstacle for some real-life applications, especially when the tour needs to be generated in real-time. The objective, in this thesis, is to find a near-optimal TSP tour with a reduced set of edges in the complete graph. In particular, the following problems are investigated: which subset of edges can be produced in a shorter time comparing to the time for generating the complete graph? Is there a subset of edges in the complete graph that results in a better near-optimal tour than other sets? With a non-complete graph, which improvement algorithms work better? In this thesis, we study six algorithms to generate subsets of edges in a complete graph. To evaluate the proposed algorithms, extensive experiments are conducted with the well-known TSP data in a TSP library. In these experiments, we evaluate these algorithms in terms of tour quality, time and scalability

The development of a weighted directed graph model for dynamic systems and application of Dijkstra’s algorithm to solve optimal control problems.

Master of Science (Chemical Engineering). University of KwaZulu-Natal. Durban, 2017.Optimal control problems are frequently encountered in chemical engineering process control applications as a result of the drive for more regulatory compliant, efficient and economical operation of chemical processes. Despite the significant advancements that have been made in Optimal Control Theory and the development of methods to solve this class of optimization problems, limitations in their applicability to non-linear systems inherent in chemical process unit operations still remains a challenge, particularly in determining a globally optimal solution and solutions to systems that contain state constraints. The objective of this thesis was to develop a method for modelling a chemical process based dynamic system as a graph so that an optimal control problem based on the system can be solved as a shortest path graph search problem by applying Dijkstra’s Algorithm. Dijkstra’s algorithm was selected as it is proven to be a robust and global optimal solution based algorithm for solving the shortest path graph search problem in various applications. In the developed approach, the chemical process dynamic system was modelled as a weighted directed graph and the continuous optimal control problem was reformulated as graph search problem by applying appropriate finite discretization and graph theoretic modelling techniques. The objective functional and constraints of an optimal control problem were successfully incorporated into the developed weighted directed graph model and the graph was optimized to represent the optimal transitions between the states of the dynamic system, resulting in an Optimal State Transition Graph (OST Graph). The optimal control solution for shifting the system from an initial state to every other achievable state for the dynamic system was determined by applying Dijkstra’s Algorithm to the OST Graph. The developed OST Graph-Dijkstra’s Algorithm optimal control solution approach successfully solved optimal control problems for a linear nuclear reactor system, a non-linear jacketed continuous stirred tank reactor system and a non-linear non-adiabatic batch reactor system. The optimal control solutions obtained by the developed approach were compared with solutions obtained by the variational calculus, Iterative Dynamic Programming and the globally optimal value-iteration based Dynamic Programming optimal control solution approaches. Results revealed that the developed OST Graph-Dijkstra’s Algorithm approach provided a 14.74% improvement in the optimality of the optimal control solution compared to the variational calculus solution approach, a 0.39% improvement compared to the Iterative Dynamic Programming approach and the exact same solution as the value–iteration Dynamic Programming approach. The computational runtimes for optimal control solutions determined by the OST Graph-Dijkstra’s Algorithm approach were 1 hr 58 min 33.19 s for the nuclear reactor system, 2 min 25.81s for the jacketed reactor system and 8.91s for the batch reactor system. It was concluded from this work that the proposed method is a promising approach for solving optimal control problems for chemical process-based dynamic systems

A Specific Network Link and Path Likelihood Prediction Tool

Communications have always been a crucial part of any military operation. As the pace of warfare and the technological complexity of weaponry have increased, so has the need for rapid information to assess battlefield conditions. Message passing across a network of communication nodes allowed commanders to communicate with their forces. It is clear that an accurate prediction of communication usage through a network will provide commanders with useful intelligence of friendly and unfriendly activities. Providing a specific network link and path likelihood prediction tool gives strategic military commanders additional intelligence information and enables them to manage their limited resources more efficiently. In this study, Dijkstra\u27s algorithm has been modified to allow the Queueing Network Analyzer\u27s (QNA) analysis output to act as a node\u27s goodness metric. QNA\u27s calculation of the expected Total Sojourn Time for the completion of queueing and service in a node provides accurate measurement of expected congestion. The modified Dijkstra\u27s algorithm in the Generalized Network Analyzer (GNA) is verified and empirically validated to properly deliver traffic. It appropriately generates the fastest traffic path from a start node to a destination node. This implementation includes notification if input parameters exceed the network\u27s processing capability. GNA\u27s Congestion Control displays notification and informs the user certain network input parameters must be lowered (PTR or BSTR) or where certain nodes must be improved to maintain node stability. With this unstable node identification, users can determine which node needs attention and improvements. Once this instability is removed, a good QoS is achieved and analysis proceeds

Network Flows

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Scheduled routing for the NuMesh

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1994.Includes bibliographical references (leaves 66-68).by Milan Singh Minsky.M.S