T: A Heuristic Search Based Path Planning Algorithm for Temporal Logic Specifications

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.

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.

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.

A theorem on the expected complexity of dijkstra's shortest path algorithm

Efficient implementations of Dijkstra's shortest path algorithm are investigated. A new data structure, called the radix heap , is proposed for use in this algorithm. On a network with n vertices, m edges, and nonnegative integer arc costs bounded by C , a one-level form of radix heap gives a time bound for Dijkstra's algorithm of O ( m + n log C ). A two-level form of radix heap gives a bound of O ( m + n log C /log log C ). A combination of a radix heap and a previously known data structure called a Fibonacci heap gives a bound of O ( m + n a @@@@log C ). The best previously known bounds are O ( m + n log n ) using Fibonacci heaps alone and O ( m log log C ) using the priority queue structure of Van Emde Boas et al. [ 17].

Throughout history, the primary means of transportation for humans has been on foot. We present a software tool which can help visualize and predict where historical trails might lie through the use of a human-centered cost metric, with an emphasis on the ability to generate paths which traverse several thousand kilometers. To accomplish this, various graph simplification and path approximation algorithms are explored. We show that it is possible to restrict the search space for a path finding algorithm while not sacrificing accuracy. Combined with a multi-threaded variant of Dijkstra's shortest path algorithm, we present a tool capable of computing a path of least caloric cost across the contiguous US, a dataset containing over 19 billion datapoints, in under three hours on a 2.5 Ghz dual core processor. The potential archaeological and historical applications are demonstrated on several examples.

We describe a novel global path planning method for autonomous qualitative navigation in indoor environments. Global path planning operates on top of a qualitative map of the environment that describes variations in sensor behavior between adjacent regions in space. The method takes into consideration the global topology of the environment and applies a set of criteria that can minimize the errors in the navigational accuracy of a robotic wheelchair. Our approach uses a modified version of the Dijkstra's shortest path algorithm that takes into consideration the curvature of the trajectory and the off-wall distance of the map points. The algorithm computes in real-time a set of optimal paths for reaching the destination. We have tested our global path planning method in simulation in representative indoor environments with above average complexity. Based on these experiments we have determined empirically a set of values for the parameters of the algorithm that almost always lead to the selection of optimal paths in these environments.

In this paper, we present an obstacle avoiding smooth path planning method based on Voronoi diagram and composite Bezier curve algorithm which obtains the curvature bounded path with small length. In our algorithm, a Voronoi diagram is constructed according to the global environment. The piecewise linear rough path in the Voronoi diagram which keeps away from the obstacles is obtained by performing Dijkstra's shortest path algorithm. Dynamic programming is employed to subdivide the nodes on the piecewise linear path into control point subsequences to generate a collision free composite Bezier curve which satisfies the curvature constraint and approaches minimal path length.

An O( mlog log D) algorithm for shortest paths

In this paper, we present a fast and robust algorithm for centerline extraction in blood vessels. The algorithm is suitable for catheter simulation in CT data of blood vessels. It creates an initial centerline based on two user-defined points (start- and endpoint). For curved vessel structures, this initial centerline is computed by Dijkstra's shortest path algorithm. For linear vessel structures, the algorithm directly connects the start- and the endpoint to get the initial centerline. Thereafter, this initial path will be aligned in the blood vessel, resulting in the vessels centerline (i.e. an optimal catheter simulation path). The alignment is done by an active contour model combined with polyhedra placed along it. Results of the proposed centerline algorithm are demonstrated for CTA with variations in anatomy and location of pathology.

The logic, implementation, and analysis of a network design approach, lowest measure paths, are discussed. The approach was conceived in order to design a signaling network dedicated to government use. By intelligently picking a subset of facility routes from the large pool of AT&T private line and commercial signaling networks using Dijkstra's shortest path algorithm, the approach generates designs that are nearly as survivable and robust as the full pool. >

Numerical simulation of Ground penetrating radar (GPR) signals is potentially valuable in both survey design and data interpretation. We develop a method for numerically synthesizing GPR received signals using geometrical ray theory. The GPR reflected ray tracing scheme is implemented using wave front expanding method, based on Fermat's principle, reciprocity principle, and Dijkstra's shortest path algorithm. This method is good for complex layered models with inhomogeneous material and undulate interfaces, and can trace all reflected ray paths from one non-planar interface at one time, for a pair of source and receiver. Simulation experiments show it is effective.

Most applications use distance as a weight to solve the shortest path problem. We employed a variety of parameters in this paper, including (Route Distance, Speed, and Capacity of the Road, and the time it takes each trip to the road). The major goal of this study is to determine the most effective approach for communicating this essential spatial information to end-users using GIS software. To discover the best route, most algorithm for best route (Dijkstra's shortest path algorithm, Euler's algorithm, etc.) are utilized. The proposed upgraded approach was applied to the Baghdad city road network as a case study. Baghdad has a problem in Processes for urban transportation planning are being implemented, particularly in terms of selecting appropriate transportation policies to address mobility issues. The Origin - Destination Matrix is a crucial component of the transportation planning process. One of the necessary aims of transportation studies in Baghdad city is the O-D matrix, which is the travel demand between (central Baghdad city and the commercial centers). The findings of this study can help local transportation authority's choose the best transportation policy, maximize income, and better manage resources.

A way to apply the shortest path ray tracing (SPR) method to irregularly tetrahedralized velocity structure and its efficiency are described. SPR is the ray tracing method utilizing Dijkstra's shortest path algorithm in network graph theory. The tetrahedralization by Delaunay tessellation is one of the irregular parameterization of 3D velocity structure in travel time tomography. The irregular parameterization has great advantage of flexible expression of velocity structure though the computational costs in ray-tracing are relatively high. The hybrid ray tracing between SPR (for initialization) and pseudo-bending (for optimization) might be more economic. It has been known as the well proven scheme in the sense of the simplicity and robustness. Though SPR was originally developed under regular parameterization, it can easily be expanded to irregular parameterized structure without any theoretical modification. We propose a simple design of network for SPR that conforms the shape of tetrahedron. Generally, the cost and accuracy of SPR depends on the network design. In this paper, we have carried out a synthetic examination with a complex velocity model to assess the cost and accuracy of SPR with irregular network. Result reveals that the proposed ray tracing method is practically economic and accurate (almost the same accuracy as SPR under the regular cubic cell model). Further, it has potential to obtain more accuracy by lower costs due to the economical network integrated with flexible element size.

Report of the Session on Network Flow, Assignment and Travelling Salesman Problems