The Improved Dijkstra's Shortest Path Algorithm and Its Application

AbstractThe shortest path problem exists in variety of areas. A well known shortest path algorithm is Dijkstra's, also called “label algorithm”. Experiment results have shown that the “label algorithm” has the following issues: I.. Its exiting mechanism is effective to undigraph but ineffective to digraph, or even gets into an infinite loop; II. It hasn’t addressed the problem of adjacent vertices in shortest path; III.. It hasn’t considered the possibility that many vertices may obtain the “p-label” simultaneously. By addressing these issues, we have improved the algorithm significantly. Our experiment results indicate that the three issues have been effectively resolved

Calculating path algorithms

AbstractA calculational derivation is given of two abstract path algorithms. The first is an all-pairs algorithm, two well-known instances of which are Warshall's (reachability) algorithm and Floyd's shortest-path algorithm; instances of the second are Dijkstra's shortest-path algorithm and breadth-first/depth-first search of a directed graph. The basis for the derivations is the algebra of regular languages

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

COMPARATIVE ANALYSIS AND IMPLEMENTATION OF DIJKSTRA'S SHORTEST PATH ALGORITHM FOR EMERGENCY RESPONSE AND LOGISTIC PLANNING

TransRoute: a web-based vehicle route planning application is proposed in this paper. This application leverages existing input-output (I/O) efficient implementations of shortest path algorithms (SPAs) to implement the proposed system that will fundamentally address the problems experienced in moving people, goods and services from one location to another. A number of SPAs are evaluated using landau notations. Main functionalities of the system will be implemented as a web-enabled geographic information system (GIS) application based on open-source technologies and object-oriented software development methodology using unified modeling language. Pilot implementation is done based on spatial data of three selected states in Nigeria, pulled from web-based mapping tools like Google Maps and Microsoft Bings respectively. In conclusion, the Dijkstra's algorithm implemented with double bucket dynamic data structure is selected for implementing the proposed route planning system, as past research efforts has proven that it is the fastest with run-time improvements from O(m + n/log C) to O(m) respectively. http://dx.doi.org/10.4314/njt.v36i3.3

Heuristics for Bandwidth Reservation in Multihop Wireless Networks

We propose three heuristics to compute QoS routes in a multihop wireless networks considering interferences constraints. It has been proved that reservation under such conditions is an NP-complete problem. Our heuristics are based on Dijkstra's shortest path algorithm in which we integrate the notion of bandwidth capacity in order to satisfy flows requirements.We show with several simulations that these heuristics not only allows computation of routes that save bandwidth of nodes with low capacity but also that network can handle more QoS-flows

Optimization algorithms for shortest path analysis

Discrete optimization algorithms exist for analysis of network optimization of flow problems. Computer programs written from these algorithms can be used for local area network analysis of point-to-point computer networks, transportation networks, resource allocation, distribution, and production scheduling. One aspect of a network that can be optimized using discrete optimization algorithms is the length of the path that data will take when traveling through the network. One node in the network signifies the source node and a second node is the sink or destination. The object is to find the shortest path between the two nodes. The definition of shortest path depends on the quantity analyzed in the network. Shortest path can represent the fastest path, most cost-efficient path, most fuel-efficient path, etc. Also, different levels of computation may be required. It may be necessary to find the shortest path between two nodes in a network, the shortest path between a source node and all other nodes in a network, or the shortest path between all pairs of nodes in a network. The complexity, performance, and results of different optimization methods can be compared using a series of network models. A comparison of the algorithms researched and results of the computer analysis will be shown

Controlled transitions between orbits in nonlinear systems

In recent years, several methods of controlling chaotic systems have been developed and implemented. The main idea in each method is to stabilize on an orbit around a chaotic attractor, which generally has a dense set of unstable periodic orbits. One such control scheme repeatedly applies a sequence of controls to a double scroll oscillator. Most control sequences result in the stabilization of an approximate unstable periodic orbit regardless of initial condition. These stabilized periodic orbits are called chaotic unstable periodic orbit-lets (cupolets). Due to the nature of cupolets, it is possible to switch between cupolets, and thus periodic orbits, by changing from one control sequence to another. Switching between orbits is a continuous and smooth transition, but may involve significant chaotic transients. We will present three methods of transitioning between cupolets and suggest some applications of this procedure. The first method involves applying the second control sequence at a location on the first orbit. The second method is a zero-length transition which can be used if two cupolets intersect. The third method is applicable when transitioning between non-intersecting cupolets. This method switches between intermediate cupolets in an efficient controlled manner in getting from one cupolet to the next

Wind optimal flight trajectories to minimise fuel consumption within a 3 dimensional flight network

This paper assesses the potential fuel savings benefits that can be gained from wind optimal flight trajectories. This question is posed on a 3 dimensional fixed flight network consisting of discrete waypoints which is representative of the size of Europe. The optimisation implements Dijkstra's shortest path algorithm to compute the minimum fuel burn route through a network and compares this to the fuel burn for the shortest distance route. Particular effort is applied to testing the repeatability and robustness of the results. This is achieved through a sensitive analysis based on a number of identified model parameters relating to the setup of the flight network. The results of this study show fuel savings between 1.0%-10.3%, and suggest that the benefits of wind optimal flight trajectories are significant