Theshortest Path Research Articles

A novel ant colony optimization algorithm for the shortest-path problem in traffic networks

The Ant Colony Optimization (ACO) algorithm is a metaheuristic nature-inspired technique for solving various combinatorial optimization problems. The shortest-path problem is an important combinatorial optimization problem in network optimization. In this paper, a novel algorithm based on ACO to solve the single-pair shortest-path problem in traffic networks is introduced. In this algorithm, a new strategy is developed to find the best solution in a local search, by which the ants seek the shortest path using both a pheromone-trail-following mechanism and an orientation-guidance mechanism. A new method is designed to update the pheromone trail. To demonstrate the good performance of the algorithm, an experiment is conducted on a traffic network. The experimental results show that the proposed algorithm produces good-quality solutions and has high efficiency in finding the shortest path between two nodes; it proves to be a vast improvement in solving shortest-path problems in traffic networks. The algorithm can be used for vehicle navigation in intelligent transportation systems.

Prediction-Based Path Planning with Obstacle Avoidance in Dynamic Target Environment

In this paper, a new algorithm for mobile robot navigation and polygonal obstacles avoidance in dynamic target environment is introduced. In the dynamic target path planning theagent (robot) trying to reach a moving target in minimum pathcost. The introduced algorithm which called Prediction-basedpath planning with obstacle avoidance in dynamic target environment planning a path to a moving target by predicting the nexttarget location, then computing a path from the robot current location to the predicted target location representing each visibleobstacle by the smallest circle that enclosing the polygon obstacle,then determine the visible tangents between the robot and the circular obstacle that intersect its shortest path and compute theshortest path. Three target movement scenarios were suggestedand tested in different environment conditions. The results showthat the target was reached in all scenarios and under all environment conditions with good path cost.

Cutting patterns of membrane structures

Membrane structures are very lightweight and highly optimized structures. Due to the constant stress state, strength of materials is used optimally. In order to prevent the occurrence of large deformations even for small external loads, membrane structures are designed as a double curved surfaces and are stabilized by applying prestress. Minimal surfaces has zero mean curvature and the basic advantage is that the stress at all points and directions is equal and there are no extreme stresses anywhere on the surface. Also have minimal area for the given contour, so the weight and amount of material is reduced to minimum, which make them suitable for application in architecture. Practical realization involve process of cutting pattern generation, which divide surfaces in parts that are developable surfaces. When patterns are assembled and prestressed they provide three-dimensional surface. Ideally, the cutting lines should follow the geodesics lines. We use geodesics as the shortest path between two points on a surface. In the article we give method for finding shortest paths on polygonal representations of surfaces follows continual Dijkstra paradigm which, on some conditions, can give improved accuracy on a computer despite the restriction of available memory and execution time.

ON THE SIGNED TOTAL DOMINATION NUMBER OF GENERALIZED PETERSEN GRAPHS P(n, 2)

Abstract. Let G = (V,E) be a graph. A function f : V → {−1,+1}defined on the vertices of G is a signed total dominating function if thesum of its function values over any open neighborhood is at least one.The signed total domination number of G, γ st (G), is the minimum weightof a signed total dominating function of G. In this paper, we study thesigned total domination number of generalized Petersen graphs P(n,2)and prove that for any integer n ≥ 6, γ st (P(n,2)) = 2⌊ n3 ⌋ + 2t, wheret ≡ n(mod 3) and 0 ≤ t ≤ 2. 1. IntroductionFor notation and graph theory terminology we in general follow [5]. Spe-cially, let G be a graph with vertex set V (G) and edge set E(G). Let v be a ver-tex in V (G). The openneighborhood of v is N G (v) = {u ∈ V (G) | uv ∈ E(G)}.If the graph G is clear from the text, we simply write V , E and N(v) ratherthan V (G), E(G) and N G (v). If X ⊆ V , then hXi is the subgraph induced byX. The distance d(x,y) between two vertices x and y in G is the length of theshortest path from x to y. For a real-valued function f : V → R, the weight off is w(f) =P

Platform for capacity reservation in IP networks

The fast development of multimedia devices and services causes the need for increase of the transport capacity of packet networks. OSPF-TE uses both the information about network topology and the link utilization when finding the routing path. Accordingly, it might find path even in the cases when the shortest path routing would cause overloaded link and dropped packets. In this paper we develop the platform for capacity reservation in IP networks. We implement OSPF-TE protocol as an extension of the existing OSPF. In addition, the basic functionalities of the reservation protocol and the user interface are implemented. We present the simulation environment for the verification of our implementation and for the analysis of various routing algorithms based on the information conveyed by OSPF-TE.

Incremental Convex Hull as an Orientation to Solving theShortest Path Problem

The following problem is very classical in motion planning: Let a and b be two vertices of a polygon and P (Q, respectively) be the polyline formed by vertices of the polygon from a to b (from b to a, respectively) in counterclockwise order. We find the Euclidean shortest path in the polygon between a and b. In this paper, an efficient algorithm based on incremental convex hulls is presented. Under some assumption, the shortest path consists of some extreme vertices of the convex hulls of subpolylines of P (Q, respectively), first to start from a, advancing by vertices of P, then by vertices of Q, alternating until the vertex b is reached. Each such convex hull is delivered from the incremental convex hull algorithm for a subpolyline of P (Q, respectively) just before reaching Q (P, respectively). Unlike known algorithms, our algorithm does not rely upon triangulation and graph theory. The algorithm is implemented by a C code then is illustrated by some numerical examples. Therefore, incremental convex hull is an orientation to determine the shortest path. This approach provides a contribution to the solution of the open question raised by J. S. B. Mitchell in J. R. Sack and J. Urrutia, eds, Handbook of Computational Geometry, Elsevier Science B. V., 2000, p. 642. determining convex ropes in robotics (for determining convex hulls, respectively) were introduced in (6) and (7) ((8), respectively). These problems are variations of the shortest path problem and thus can be solved without resorting to a linear-time triangulation algorithm and without resorting to graph theory. Geometrically, we determine the shortest path connecting two points a and b that avoids the obstacles - polylines P and Q. Assume without loss of generality that a and b are the first and the final vertices of P and Q, respectively. In this paper, an O(|P||Q|) time algorithm for determining the shortest path, without resorting to a linear-time triangulation algorithm and without resorting to graph theory, is presented, using the method of incremental convex hull, where |P| (|Q|, respectively) is the number of vertices of P (Q, respectively). Under an assumption on links to P and Q, the shortest path consists of the extreme vertices of the convex hulls downward, first advancing on one convex hull formed by vertices of P including a, then on the other formed by vertices of Q, alternating until the vertex b is reached. Each such convex hull is delivered from the incremental convex hull algorithm for a subpolyline of P (Q, respectively) just before reaching Q (P, respectively). Therefore, incremental convex hull is an orientation to determine the shortest path. The algorithm is implemented by a C code and is illustrated by some numerical examples. This paper also provides a contribution to the solution of the Mitchell's open question above.

Epidemic metapopulation model with traffic routing in scale-free networks

In this paper, we propose a model incorporating both the traffic routing dynamics and thevirus prevalence dynamics. In this model, each packet may be isolated from the networkon its transporting path, which means that the packet cannot be successfullydelivered to its destination. In contrast, a successful transport means that a packetcan be delivered from source to destination without being isolated. The effectsof model parameters on the delivery success rate and the delivery failure rateare intensively studied and analyzed. Several routing strategies are performedfor our model. Results show that the shortest path routing strategy is the mosteffective for enhancing the delivery success rate, especially when each packet isonly allowed to be delivered to the neighbor with the lowest degree along theshortest path. We also find that, by minimizing the sum of the nodes’ degreealong the transporting path, we can also obtain a satisfactory delivery successrate.

An Investigation of Using Parallel Genetic Algorithm for Solving the Shortest Path Routing Problem

Problem statement: Shortest path routing is the type of routing widely used in computer network nowadays. Even though shortest path routing algorithms are well established, other alternative methods may have their own advantages. One such alternative is to use a GA-based routing algorithm. According to previous researches, GA-based routing algorithm has been found to be more scalable and insensitive to variations in network topologies. However, it is also known that GA-based routing algorithm is not fast enough for real-time computation. Approach: To improve the computation time of GA-based routing algorithm, this study proposes a coarse-grained parallel GA routing algorithm for solving the shortest path routing problem. The proposed algorithm is evaluated using simulation where the proposed algorithm is executed on networks with various topologies and sizes. The parallel computation is performed using an MPI cluster. Three different experiments were conducted to identify the best value for the migration rate, the accuracy and execution time with respect to the number of computing nodes and speedup achieved as compared to the serial version of the same algorithm. Results: The result of the simulation shows that the best result is achieved for a migration rate around 0.1 and 0.2. The experiments also show that with larger number of computing nodes, accuracy decreases linearly, but computation time decreases exponentially, which justifies the use parallel implementation of GA to improve the speed of GA-based routing algorithm. Finally, the experiments also show that the proposed algorithm is able to achieve a speedup of up to 818.11% on the MPI cluster used to run the simulation. Conclusion/Recommendations: We have successfully shown that the performance of GA-based shortest path routing algorithm can be improved by using a coarse-grained parallel GA implementation. Even though in this study the proposed algorithm is executed using an MPI cluster, the algorithm is also applicable to other parallel architecture such as multi-core CPU, multi-processor or GPGPU. A future work would be to evaluate the performance of the proposed algorithm on these other parallel architectures.

An efficient strategy for enhancing traffic capacity by removing links in scale-freenetworks

An efficient link-removal strategy, called the variance-of-neighbor-degree-reduction (VNDR)strategy, for enhancing the traffic capacity of scale-free networks is proposed in thispaper. The VNDR strategy, which considers the important role of hub nodes,balances the amounts of packets routed from each node to the node’s neighbors.Compared against the outcomes of strategies that remove links among hub nodes, ourresults show that the traffic capacity can be greatly enhanced, especially under theshortest path routing strategy. It is also found that the average transport time iseffectively reduced by using the VNDR strategy only under the shortest path routingstrategy.

Shortest path algorithms

Theshortest path problem is considered from a computational point of view. Eight algorithms which solve theshortest path tree problem on directed graphs are presented, together with the results of wide-ranging experimentation designed to compare their relative performances on different graph topologies. The focus of this paper is on the implementation of the different data structures used in the algorithms. A "Pidgin Pascal" description of the algorithms is given, containing enough details to allow for almost direct implementation in any programming language. In addition, Fortran codes of the algorithms and of the graph generators used in the experimentation are provided on the diskette.