Routing in quantum networks with end‐to‐end knowledge

The authors present a path-planning algorithm to find the least-cost path along the WVD (weighted Voronoi diagram) based on Dijkstra's shortest path algorithm, where the cost of an edge is, in this case, the risk of transversing the edge. By imposing a discrete graph over the area of interest, the authors obtain a reduction from a continuous problem to a combinatorial problem. If the start or goal position does not lie on this graph, it is retracted by either the path of shortest distance or the path of steepest descent. Unfortunately, the WVD is not connected in some cases, and they have to enforce connectivity. With a practical aim in mind, the authors give a simple and easily computed path, connecting the disconnected components by the shortest distance path or by a circular path. With suitable preprocessing, they keep the run-time cost of path planning to O(n/sup 2/ log n), including the cost of retraction of both the start and goal positions and the cost of Dijkstra's shortest path (or least-cost) algorithm. The authors demonstrate a potential application of the weighted Voronoi diagram as a heuristic in least-risk motion planning. >

This paper extends the well-known Dijkstra's shortest path algorithm to consider not only the edge weights but also the node weights for a graph derived from the underlying SDN topology. We use Pyretic to implement the extended Dijkstra's algorithm and compare it with the original Dijkstra's algorithm and the unit-weighted Dijkstra's algorithm under the Abilene network topology in terms of end-to-end latency with the Mininet tool. As shown by the comparisons, the extended Dijkstra's algorithm outperforms the other algorithms.

One of the key issues in providing end-to-end quality of service (QoS) guarantees in today's networks is how to determine a feasible route that satisfies a set of constraints. In general, finding a path subject to multiple constraints is an NP-complete problem that cannot be exactly solved in polynomial time. Accordingly, several heuristics and approximation algorithms have been proposed for this problem. Many of these algorithms suffer from either excessive computational cost or low performance. In this paper, we propose a fuzzy-logic based algorithm for finding a bandwidth-delay-constrained path by Dijkstra's shortest path algorithm. The main objective of Fuzzy QOS Routing Algorithm (FQRA) is to reduce packet loss and increase overall network utilization. To achieve this objective, the algorithm at First, eliminates all links with a bandwidth less than the requirement so that any paths in the resulting graph will satisfy the bandwidth constraint. Then, a new single parameter with the aid of Fuzzy Logic is generated from inputs bandwidth and delay. The Shortest path calculated by Dijkstra's algorithm based on new metric. Simulation results show that FQRA outperforms several earlier algorithms in terms of overall network utilization and packet loss. The worst-case computational complexity of this algorithm is within a logarithmic number of calls to Dijkstra's shortest path algorithm, equal with O(n2) for a network graph with n nodes.

This paper deals with Dijkstra's shortest path algorithm and with the possibilities of speeding-up this algorithm. This algorithm is a breadth-first-search algorithm. The search spreads circularly around the source node in order to find the shortest path from the source node to other nodes. Each following iteration is based on the results of the previous iteration, therefore parallelization of such an algorithm is complicated. The parallel Dijkstra algorithm, proposed in this paper, is based on the bidirectional Dijkstra algorithm and popular multicore technology. Such a technology enables to create a parallel algorithm based on the shared memory and most of the time for data synchronization thereby is saved. The proposed algorithm has been tested using the real road network data. The proposed parallel algorithm is almost 3 times faster than the standard Dijkstra algorithm.

When designing routing protocols for space-based networks, we must take into consideration the unique characteristics of such networks. Since space-based networks are inherently sparse with constrained resources, one needs to design smart routing algorithms that use the resources efficiently to maximize network performance. In Space Exploration Missions, the trajectories and orbits of spacecraft are predetermined, thus communication opportunities are predictable. This a-priori knowledge can be used to the advantage of scheduling and routing. In this paper, we focus on analyzing Contact Graph Routing (CGR) for space-based networks. CGR makes use of the predictable nature of the contacts to make routing decisions. Mars and Lunar mission-like scenarios were used in our simulations to gather statistics on routing protocol performance in terms of delay and buffer usage. We provide improvements to the underlying cost function of CGR to avoid routing loops and suggest applying Dijkstra's shortest path algorithm for path selection. The cost function change was incorporated into the latest Internet Draft posted for CGR. Dijkstra's shortest path algorithm was successfully implemented and tested in NASA's Interplanetary Overlay Network (ION) implementation of the DTN protocols.

The fundamental path planning problem for a mobile robot involves generating a trajectory for point-to-point navigation while avoiding obstacles. Heuristic-based search algorithms like A* have been shown to be efficient in solving such planning problems. Recently, there has been an increased interest in specifying complex path planning problem using temporal logic. In the state-of-the-art algorithm, the temporal logic path planning problem is reduced to a graph search problem, and Dijkstra's shortest path algorithm is used to compute the optimal trajectory satisfying the specification.The A* algorithm, when used with an appropriate heuristic for the distance from the destination, can generate an optimal path in a graph more efficiently than Dijkstra's shortest path algorithm. The primary challenge for using A* algorithm in temporal logic path planning is that there is no notion of a single destination state for the robot. We present a novel path planning algorithm T* that uses the A* search procedure opportunistically to generate an optimal trajectory satisfying a temporal logic query. Our experimental results demonstrate that T* achieves an order of magnitude improvement over the state-of-the-art algorithm to solve many temporal logic path planning problems in 2-D as well as 3-D workspaces.

Ball-end milling is widely used in five-axis high-speed machining. The abrupt change of tool orientations or rotary axes movements will scrap the workpiece. This research presents a smoothing method of rotary axes movements within the feasible domains of the rotary-axes space. Most existing smoothing methods of tool orientation or rotary axes movements employ the Dijkstra's shortest path algorithm. However, this algorithm requires extensive computations if the number of the cutter locations is large or the sampling resolution in the feasible regions is high. Moreover, jumps in the results obtained with the Dijkstra's shortest path algorithm may occur, because the optimization problem has to be converted from a continuous problem into a discrete problem when using this algorithm. The progressive iterative approximation (PIA) method incorporating smoothness terms is established as a gradient-based optimization method to smooth the rotary axes movements in this research. Then a gradient-based differential evolution (DE) algorithm, combining the global exploration feature of the DE algorithm and the local searching ability of the gradient-based optimization method, is developed to solve the smoothing model. The validity and effectiveness of the proposed approach are confirmed by numerical examples.

In this paper we propose a natural straight forward implementation of Dijkstra's shortest path algorithm on a model of associative parallel processors of the SIMD type with bit-serial (or vertical)...

In this paper we propose a natural straight forward implementation of Dijkstra's shortest path algorithm on a model of associative parallel processors of the SIMD type with bit-serial (or vertical) processing (the STAR-machine). In addition, we show how to extend this implementation for restoring the shortest path from the source vertex to a given vertex. These algorithms of implementation are represented as the corresponding STAR procedures whose correctness is verified and time complexity is evaluated.

This paper presents the effects of shortest path routing in wavelength-routed optical WDM networks; in particular we evaluated the effect of this routing scheme on the performance of wide all-optical WDM networks. Given a session request and a number of available wavelengths on each optical fiber, the routing and wavelength assignment (RWA) problem is to establish a lightpath (routing subproblem), i.e., to determine a path between two nodes, and also assign a wavelength along this path (wavelength assignment subproblem), so to maximize the number of satisfied requests for connections by taking into account some constraints. This study focuses on the routing subproblem in wavelength-routed all-optical WDM networks. We use Dijkstra's shortest path algorithm, to determine the shortest paths in terms of the number of hops (we assume that the links have the same weight, uniform traffic) from the source to other nodes in the network. We evaluate, for the first time, the performance of this algorithm for optical routing and we study the impact on the load distribution over the wide all-optical WDM network links. We also implement a simulation interface to evaluate this algorithm in wide all-optical WDM networks (different optical networks topologies were used in the simulation). This paper describes the inadequacy of the use of standard Dijkstra's shortest path routing, as it produces more unbalanced routes over the network links and unnecessary link overload.

Today, most routing problems are solved using Dijkstra's shortest path algorithm. Many efficient implementations of Dijkstra's algorithm exist and can handle large networks in short runtimes. Despite these advances, it is difficult to incorporate user-specific conditions on the solution when using Dijkstra's algorithm. Such conditions can include forcing the path to go through a specific node, forcing the path to avoid a specific node, using any combination of inclusion/exclusion of nodes in the path, etc. In this paper, we propose a new approach to solving the shortest path problem using advanced Boolean satisfiability (SAT) techniques. SAT has been heavily researched in the last few years. Significant advances have been proposed and has lead to the development of powerful SAT solvers that can handle very large problems. SAT solvers use intelligent search algorithms that can traverse the search space and efficiently prune parts that contain no solutions. These solvers have recently been used to solve many problems in engineering and computer science. In this paper, we show how to formulate the shortest path problem as a SAT problem. Our approach is verified on various network topologies. The results are promising and indicate that using the proposed approach can improve on previous techniques

This paper proposes a parallel shortest path-searching algorithm and implements it on a newly structured parallel reconfigurable processor, DAPDNA-2 (IPFlex Inc). Routing determines the shortest paths from the source to the ultimate destination through intermediate nodes. In open shortest path first (OSPF), Dijkstra's shortest path algorithm, which is the conventional one, finds the shortest paths from the source on a program counter-based processor. The calculation time for Dijkstra's algorithm is O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) when the number of nodes is N. When the network scale is large, calculation time required by Dijkstra's algorithm increases rapidly. It's very difficult to compute Dijkstra's algorithm in parallel because of the need for previous calculation results, so Dijkstra's algorithm is unsuitable for parallel processors. Our proposed scheme finds the shortest paths using a simultaneous multi-path search method. In contrast with Dijkstra's algorithm, several nodes can be determined at one time. Moreover, we partition the network into different groups (network groups) and find the all-node pair's shortest path in each group using a pipeline operation. Networks can be abstracted, and the shortest paths in very large networks can be found easily. The proposed scheme can decrease calculation time from O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) to O(N) using a pipeline operation on DAPDNA-2. Our simulations show that the proposed algorithm uses 99.6% less calculation time than Dijkstra's algorithm. The proposed algorithm can be applied to the very large Internet network designs of the future.

Computing shortest path between nodes in a given directed graph is a very practical problem. Among the various shortest path algorithms, Dijkstra's shortest path algorithm is said to have better performance with regard to runtime. The speedup techniques when applied to shortest path algorithm were naturally improved the speedup of the algorithm there by the system performance. The combined speedup techniques are utilized along with Dijkstra's algorithm to further improve the performance in terms of runtime and number of vertices visited in the graph. The speedup techniques namely arc flags and bidirectional search were combined (COAB) and the speedup was measured with respect to runtime and number of nodes visited. The pre-processing phase of arc flags was parallelized to improve the performance of the system. The results were tested in random, planar and real world graphs.

본 논문은 유전자 알고리즘을 이용해서 동적으로 변하는 네트워크상에서 빠르게 최단 경로를 재탐색할 수 있는 알고리즘을 제안한다. 제안 알고리즘은 다익스트라 알고리즘과 유전자 알고리즘을 통합한 형식의 알고리즘이다. 이 제안 알고리즘은 최초 탐색 시 다익스트라(Dijkstra) 알고리즘을 이용해서 유전자 알고리즘의 초기화 과정을 용이하게 하는 선행자 배열을 정의한다. 그 후 유전자 알고리즘은 적절한 유전 연산자를 통해 동적으로 변하는 트래픽 상황에서 최적의 경로를 재탐색한다. 실험 결과를 통해 제안 알고리즘이 거대한 네트워크 데이터에 대해서 다른 유전자 알고리즘 기반의 최단경로 찾기 알고리즘이나 다익스트라 알고리즘보다 적은 계산시간으로 더 짧은 주행시간의 경로를 제시한다는 것을 보였다. This paper presents a fast and scalable re-routing algorithm that adapts to dynamically changing networks. The proposed algorithm integrates Dijkstra's shortest path algorithm with the genetic algorithm. Dijkstra's algorithm is used to define the predecessor array that facilitates the initialization process of the genetic algorithm. After that, the genetic algorithm re-searches the optimal path through appropriate genetic operators under dynamic traffic situations. Experimental results demonstrate that the proposed algorithm produces routes with less traveling time and computational overhead than pure genetic algorithm-based approaches as well as the standard Dijkstra's algorithm for large-scale networks.

A walk over the shortest path: Dijkstra's Algorithm viewed as fixed-point computation