# shortest path problem

## Top PDF shortest path problem:

### Overview of Algorithms for Shortest Path Problem

This paper presents overview of algorithms for the shortest path problem. It explains Dijkstra algorithm and Floyd-Warshalls algorithm that are explained on examples of smaller graphs. Definition of graphs, basic methods of graph presentation and their basic division are explained in fist part of the paper. Dijkstra algorithm is implemented in Java programing language. Program was made in InteliJ development environment. Algorithm is implemented on the example of graph which is made of eight nodes. Graph symbolizes smaller information and communication traffic network. Goal of program is to calculate delays from source node to all other nodes in network. Routing, in Internet traffic, is the process of choosing a path over which to send packets from source router to destination. Goal is for packets to be delivered as soon as possible, for decision making we are using shortest path algorithms as Dijsktra algorithm implemented in this paper.

### Solving shortest path problem using gravitational search algorithm and neural networks

The report for this study consists of four chapters. Chapter 1 presents an introduction to the study, problem background, objective, scope and significance of this study. Chapter 2 reviews the Shortest Path Problem Types and Applications, classic methods to solving the Shortest Path Problem, heuristic algorithms for the Shortest Path Problem, and the Gravitational Search Algorithm, which are the fundamental parts in the method proposed in this study. Chapter 3 discusses the methodology used in this study. Chapter 4 presents the results and evaluation of the results. And finally Chapter 5 is the Conclusion.

### An Extended Shortest Path Problem with Switch Cost Between Arcs

The standard shortest path problem only considers the cost on the arc, and it doesn’t consider the cost of switch- ing between arcs. But in some applications such as trans- portation networks, the switch cost between arcs does exist and is important. So it is necessary to solve the problem by considering switch cost between arcs. This paper will focus on this point. To explain the problem better, we deﬁne some notations ﬁrst.

### Z-Dijkstra’s Algorithm to solve Shortest Path Problem in a Z-Graph

In graph theory, the Shortest Path Problem (SPP) is one of the most famous problems studied and being studied by researchers. The SPP is the problem of finding a path between two vertices (or nodes) in a digraph such that the sum of the weights of its constituent edges is minimized. Thus the core problem is to find the shortest path from a source vertex S to a single destination vertex D in a directed graph and to compute the corresponding min cost. Shortest Path problems (SPP) are among the fundamental problems studied in Computational Geometry, Graph Algorithms, Geographical Information Systems (GIS), Network Optimization etc. to list a few only out of many. Sometimes the network of a real life communication

### Adapted A* Algorithm for the Shortest Path Problem with Position-Based Learning Effects

1226 | P a g e The shortest path problem is the problem of finding a path between two veracities or nodes in a graph such that sum of weights of its constituent edges are minimized. Shortest path problems (SPPs) are widespread in practical applications (e.g., logistics, transportation, robot path planning[4,5], vehicle routing[6], no-wait flow shop scheduling[7], etc.). SPP consists of finding the shortest path from the source node to the sink node in a graph. Generally, the distance, time or price of traversing of each arc is called cost. There are a large number of paths in the graph.

### Parallel Implementations for Solving Shortest Path Problem using Bellman Ford

Single source shortest path problem finds application in large domains of scientific and real world. Common applications of these algorithms are in network routing [6], VLSI design, robotics and transportation, they are also used for directions between physical locations like in google maps. Here all the applications mentioned generally involve positive weights but some applications are there where weights can be negative like currency exchange arbitrage and some other areas where, edge represents something other than merely distance between two entities. In such application areas Bellman-Ford algorithm can be used. Bellman-Ford algorithm[12] is applicable on graphs with negative weights and can also detect negative cycles where majority of algorithms fail. Bellman-Ford is also used in wireless sensor networks and other ad hoc networks as distributed Bellman Ford [7] can be used there. Distributed Bellman-Ford is also used as first ARPANET routing algorithm in 1969 [14].

### A New Approach for Solving Type-2 Fuzzy Shortest Path Problem

Abstract. In a network the arc lengths may represent time or cost. In practical situations, it is reasonable to assume that each arc length is a type-2 discrete fuzzy set. We called it the type-2 discrete fuzzy shortest path problem. In this paper we proposed an algorithm for finding shortest path and shortest path length from source node to destination node using type reduction method. We have compared our result with other measures like Hamming, Normalized Hamming, Exponential type distance measure also. An illustrative example also included to demonstrate our proposed approach.

### A Novel Approach for finding a Shortest Path Problem with Intuitionistic Fuzzy Network

The fuzzy shortest path problem is an extension of fuzzy numbers and it has many real life applications in the field of communication, robotics, scheduling and transportation. Dubois [4] introduced the fuzzy shortest path problem for the first time. Klein [6] introduced a new model to solve the fuzzy shortest path problem for sub-modular functions. Lin and Chern [8] introduced a new design to find the fuzzy shortest path problem on single most vital arc length in a network by using dynamics programming approach. Li et.al. [9] solved the fuzzy shortest path problems by using neural network approach. Chuang et al. [3] used two steps to find the shortest path from origin to destination.

### Shortest Path Problem in Network with Type-2 Triangular Fuzzy Arc Length

In traditional Shortest Path Problem (SPP) it is always determined that the parameters (Time, Cost and Distance etc.) are fixed between different nodes. But in real life situations where uncertain parameters exist, parameters are considered as fuzzy numbers. In this paper, we explained the application scope of the given fuzzy ranking function. Using this method we can determine both the fuzzy shortest path and fuzzy shortest distance from origin to destination.

### Solving All-pairs Shortest Path Problem on a Hybrid CPU-GPU Platform

At the beginning of this thesis some elementary terms from graph theory are defined as a foundation for the shortest path problem. A few varieties of the aforementioned problem are described, as well as the method of representing graphs in computer memory. After that, Floyd-Warshall algorithm for all-pairs shortest-path problem is analized in detail. Dyna- mic programming is also defined as Floyd-Warshall algorithm is a prime example of such a method. Additionally, CUDA platform for hybrid CPU-GPU computing is analized - it’s architecture, it’s advantages and disadvantages, but also, since it is a parallel computing platform, the history of parallel computing is given. Based on all the conclusions, three versions of Floyd-Warshall algorithm have been implemented: a simple C++ implementation of the algorithm which is analogous to the given pseudocode, a simple CUDA implementation which used the advantages of the graphics card architecture and an advanced (blocked) CUDA implementation which further made use of the Floyd-Warshall’s algorithm parallel nature. At the end, the experimental results of all three implementations on different sized graphs and graphs of various densities have been laid out.

### An Android Application to solve the shortest path problem using Google Services and Dijkstra's Algorithm

In this paper, I examine Dijkstra’s algorithm in the context of solving the shortest path problem. The mathematical modeling of this problem has to do with the theory of graphs. The whole system is programmed as client system using Google Services and Android OS. Google Services are used to determine the optimum path on Google map and solve the shortest path problem as alternative of Dijkstra's Algorithm.

### OpenCL Parallel Blocked Approach for Solving All Pairs Shortest Path Problem on GPU

All-Pairs Shortest Path Problem (APSP) finds a large number of practical applications in real world. This paper presents a blocked parallel approach for APSP using an open standard framework OpenCL, which provides development environment for utilizing heterogeneous computing elements of computer system and to take advantage of massive parallel capabilities of multi-core processors such as graphics processing unit (GPU) and CPU. This blocked parallel approach exploits the local shared memory of GPU, thereby enhancing the overall performance. The proposed solution is for directed and dense graphs with no negative cycles and is based on blocked Floyd Warshall (FW) and Kleene‟s algorithm. Like Floyd Warshall this approach is also in-place and therefore requires no extra memory.

### A Shortest Path Problem in an Urban Transportation Network Based on Driver Perceived Travel Time

Abstract. This paper proposes a method to solve shortest path problems in route choice processes when each link's travel time is a fuzzy number, called the Perceived Travel Time (PTT). The PTT is a subjective travel time perceived by a driver. The algorithm solves the fuzzy shortest path problem (FSPA) for drivers in the presence of uncertainty regarding route travel time. For congested networks, the method is able to nd the shortest path in terms of perceived travel time and degree of saturation (congestion) along routes at the same time. The FSPA can be used to support the fuzzication of trac assignment algorithms. The applicability of the resulting FSPA for the trac assignment was tested in conjunction with incremental trac loading and was applied to a large-scale real network. The results of the trac assignment based on the FSPA, User Equilibrium (UE) and a stochastic loading network model (Dial's assignment algorithm) were compared to the observed volume for certain links in the network. We conclude that the proposed method oers better accuracy than the UE or Dial's assignment algorithm for the network under testing. Keywords: Fuzzy sets; Perceived travel time; Route choice; Shortest path; Urban network.

### A Parallel Recursive Approach for Solving All Pairs Shortest Path Problem on GPU using OpenCL

Abstract— All-pairs shortest path problem(APSP) finds a large number of practical applications in real world. We owe to present a highly parallel and recursive solution for solving APSP problem based on Kleene’s algorithm. The proposed parallel approach for APSP is implemented using an open standard framework OpenCL which provides a development environment for utilizing massive parallel capabilities of Multi core CPU and Many-Core-Processors such as Graphics Processing Unit (GPU). Moreover due to inherent nature of data reuse in the algorithm, shared memory of these processors is exploited to achieve considerable speedup. Our experiments demonstrate a speedup gain up to 521x over NVIDIA GeForce GT 630M GPU and a speedup up to 10x over Intel Core i3-2310M CPU.The proposed OpenCL solution for APSP is for directed and dense graphs with no negative cycles. Like Floyd-Warshall (FW), this approach is also in-place in nature and therefore requires no extra space.

### Fast Computation of the Shortest Path Problem through Simultaneous Forward and Backward Systolic Dynamic Programming

A graph is a set of vertices and a collection of edges that each connects a pair of vertices. The most intuitive graph- processing problem is the shortest-path problem which is concerned with finding the lowest-cost way to get from one vertex to another [1]. The graphs under consideration are edge-weighted and have an associated path weight, the value of which is the sum of the weights of the path's edges. A prominent application of the shortest-path problem is routing in multi-hop wireless networks which employs shortest-path and graph theory-based algorithms such as dynamic programming (DP) algorithms. Every wireless channel between two nodes (vertices) is viewed as a link (edge). In dynamic (adaptive) routing, the nodes need to be notified to recalculate their routes in prompt response to topology changes. This calls for intensive parallel processing in the nodes [2] to prevent bottlenecks which counteract the high speed merits of wireless networks. The ever-increasing capacity of wireless transmission [3] necessitates node switching systems with capacity and rapid response to meet this speed demand. In this paper, we attempt to calculate the best path in each vertex by employing systolic parallel dynamic programming assuming general directed acyclic graphs (DAGs). Since a DAG is a directed graph with no

### A Novel Approach of the Shortest Path Problem Using P System

Abstract: Membrane Computing is inspired from biological cell activities as a new distributed parallel computational framework, which can be used for decreasing the time complexity of problems with high execution time. Since the usual way to reduce the time complexity of Artificial Intelligence (AI) problems is using parallel algorithms, Membrane Computing can be extensively applied. On the other hand, shortest path problem (SPP) is the most broadly method to solve the problems in AI. There have been a variety of algorithms presented, that could find a solution in a desirable time but usually are not accurate, or they are accurate but they are too slow. In Membrane Computing technique, the normal way for reducing the time complexity is using P system with active membranes that the number of membranes increases during the computation; thus, the time is traded against the space. This paper presents the first Membrane Computing technique for solving the SPP using P system with membranes division by a breadth first exploring on a grid. The theorems show the run times for breadth-first search and SPP are significantly reduced.

### Novel Approach to Fuzzy Shortest Path Problem

Abstract. The shortest path problem is an important classical network optimization problem arising from many applications including robotics, networking, and transportation. In most situations, however, some issues of a network-theoretic problem may be uncertain. In conventional shortest path problems, there always an assumption that one who takes the decision is certain about the parameters (distance, time etc.) between different possible vertices in the network G={V,E}. But while considering the real time cases, the possibility of existence of uncertainty about the parameters between different nodes is always high. In those situations, the representation of parameters are given by fuzzy numbers and here we consider the generalized trapezoidal fuzzy numbers, can be dealt with the uncertainty using fuzzy set theory. In order to provide solution for the uncertain shortest path problem, we proposed Hybrid Ant based optimization with ranking of generalized trapezoidal fuzzy numbers, which is proposed recently, as a fitness function. The proposed model is implemented using MATLAB with the test network of 30 nodes and the results reports that the algorithm converges in a more reasonable time in comparison with conventional approaches.

### The On-Line Shortest Path Problem Under Partial Monitoring

The on-line shortest path problem is considered under various models of partial monitoring. Given a weighted directed acyclic graph whose edge weights can change in an arbitrary (adversarial) way, a decision maker has to choose in each round of a game a path between two distinguished vertices such that the loss of the chosen path (defined as the sum of the weights of its composing edges) be as small as possible. In a setting generalizing the multi-armed bandit problem, after choosing a path, the decision maker learns only the weights of those edges that belong to the chosen path. For this problem, an algorithm is given whose average cumulative loss in n rounds exceeds that of the best path, matched off-line to the entire sequence of the edge weights, by a quantity that is proportional to 1/ √ n and depends only polynomially on the number of edges of the graph. The algorithm can be implemented with complexity that is linear in the number of rounds n (i.e., the average complexity per round is constant) and in the number of edges. An extension to the so-called label efficient setting is also given, in which the decision maker is informed about the weights of the edges corresponding to the chosen path at a total of m n time instances. Another extension is shown where the decision maker competes against a time-varying path, a generalization of the problem of tracking the best expert. A version of the multi-armed bandit setting for shortest path is also discussed where the decision maker learns only the total weight of the chosen path but not the weights of the individual edges on the path. Applications to routing in packet switched networks along with simulation results are also presented.