Finding Shortest Paths Research Articles

Decentralized routing on spatial networks with stochastic edge weights

We investigate algorithms to find short paths in spatial networks with stochastic edge weights. Our formulation of the problem of finding short paths differs from traditional formulations because we specifically do not make two of the usual simplifying assumptions: (1) we allow edge weights to be stochastic rather than deterministic and (2) we do not assume that global knowledge of a network is available. We develop a decentralized routing algorithm that provides en route guidance for travelers on a spatial network with stochastic edge weights without the need to rely on global knowledge about the network. To guide a traveler, our algorithm uses an estimation function that evaluates cumulative arrival probability distributions based on distances between pairs of nodes. The estimation function carries a notion of proximity between nodes and thereby enables routing without global knowledge. In testing our decentralized algorithm, we define a criterion that makes it possible to discriminate among arrival probability distributions, and we test our algorithm and this criterion using both synthetic and real networks.

Morph algorithms on GPUs

There is growing interest in using GPUs to accelerate graph algorithms such as breadth-first search, computing page-ranks, and finding shortest paths. However, these algorithms do not modify the graph structure, so their implementation is relatively easy compared to general graph algorithms like mesh generation and refinement, which morph the underlying graph in non-trivial ways by adding and removing nodes and edges. We know relatively little about how to implement morph algorithms efficiently on GPUs. In this paper, we present and study four morph algorithms: (i) a computational geometry algorithm called Delaunay Mesh Refinement (DMR), (ii) an approximate SAT solver called Survey Propagation (SP), (iii) a compiler analysis called Points-To Analysis (PTA), and (iv) Boruvka's Minimum Spanning Tree algorithm (MST). Each of these algorithms modifies the graph data structure in different ways and thus poses interesting challenges. We overcome these challenges using algorithmic and GPU-specific optimizations. We propose efficient techniques to perform concurrent subgraph addition, subgraph deletion, conflict detection and several optimizations to improve the scalability of morph algorithms. For an input mesh with 10 million triangles, our DMR code achieves an 80x speedup over the highly optimized serial Triangle program and a 2.3x speedup over a multicore implementation running with 48 threads. Our SP code is 3x faster than a multicore implementation with 48 threads on an input with 1 million literals. The PTA implementation is able to analyze six SPEC 2000 benchmark programs in just 74 milliseconds, achieving a geometric mean speedup of 9.3x over a 48-thread multicore version. Our MST code is slower than a multicore version with 48 threads for sparse graphs but significantly faster for denser graphs. This work provides several insights into how other morph algorithms can be efficiently implemented on GPUs.

Impacts of Correlations on Reliable Shortest Path Finding

This paper examines how correlations in link travel times affect reliable path finding in a stochastic network. The reliable path is defined as the path that requires the lowest travel time budget to ensure a given probability of on-time arrival. Such a path can be found by solving the shortest path problem considering on-time arrival reliability (SPOTAR). SPOTAR is solved approximately by using an approach based on Monte Carlo simulation. A major advantage of the simulation-based algorithm is its ability to deal with correlated link travel times. Through the use of a real-world network, the simulation-based algorithm is first validated by comparing it with a label-correcting algorithm that can solve the uncorrelated case exactly; the impacts of the correlations on link travel times are then examined. The results of the numerical experiments indicate that correlations affect the optimal SPOTAR solutions significantly. However, larger correlations do not always lead to larger errors in the reliable route choices that ignore them.

Modeling Developable Mesh Surface by Lofting

In the metal building and garment industries, product model is required to be or closed to be developable surface (can be flattened onto planar patterns without any distortion, tear or stretch).Current work mainly focuses on interpolating only two curves with a narrow developable strip, and lose the generality of applications in industries, which often require N (N>2) curves to determine the final shape feature, and seek one interpolated developable surface. In this paper, a new developability degree criterion is introduced first and a novel lofting algorithm is proposed to model a quasi-developable mesh surface for the given characteristic curves. The curves are first adaptively sampled and then planar triangles are tiled to interpolate all sampling points. The optimal triangulation in terms of given criterion is mapped as one shortest-path finding graph problem, which can be solved by using well-known Dijkstra’s algorithm.

Development of One-to-One Shortest Path Algorithm Based on Link Flow Speeds on Urban Networks

Finding shortest paths on time dependent networks is an important task for scheduling and routing plan and real-time navigation system in ITS. In this research, one-to-one time dependent shortest path algorithms based on link flow speeds on urban networks are proposed. For this work, first we select three general shortest path algorithms such as Graph growth algorithm with two queues, Dijkstra`s algorithm with approximate buckets and Dijkstra`s algorithm with double buckets. These algorithms were developed to compute shortest distance paths from one node to all nodes in a network and have proven to be fast and efficient algorithms in real networks. These algorithms are extended to compute a time dependent shortest path from an origin node to a destination node in real urban networks. Three extended algorithms are implemented on a data set from real urban networks to test and evaluate three algorithms. A data set consists of 4 urban street networks for Anaheim, CA, Baltimore, MD, Chicago, IL, and Philadelphia, PA. Based on the computational results, among the three algorithms for TDSP, the extended Dijkstra`s algorithm with double buckets is recommended to solve one-to-one time dependent shortest path for urban street networks.

Distributed Commuting Augmented Shortest Path Finding for Geo Spatial Database

Spatial information is a large collection of datasets referring to the real world entities. Geo Spatial information has evolved in the last decade which led to produce a vast platform in Government Administration, Scientific Analysis and other various sectors especially in disaster management (DM), site suitability of Check-dams for Irrigation Department etc. It is required to obtain imperative geographically analyzed solutions like finding shortest path between sources (i.e. location having stock of food packets, clinical remedial and therapeutic kits, etc.) to the destination (i.e. location where disaster emerges). Departmental data (i.e. village Maps) covers detailed spatial and attribute information compared to the readily available sources. Hence custom solutions based on Information Technology are required to be constructed, processed efficiently and quickly to outfit seamless performance that facilitates in mission critical incidences.

Shortest Path Finding in country using Hybrid approach of BBO and BCO

In this paper a hybrid approach of BBO and BCO technique is used to find the shortest path from source to the target point. The input data is a red band satellite image. In this image there are no prior paths and we don't have any prior information about the area. So path planning is a key factor to find out the optimized path which includes terrain mapping, obstacle detection and avoidance, and goal seeking in crosscountry using a hybrid approach of BBO and BCO techniques of Swarm Intelligence. In this hybrid approach Biogeography Based Optimization (BBO) is used for path extraction and obstacle detection from the red satellite image, morphological operation is used for smooth image and Bee Colony Optimization (BCO) algorithm is used for obstacle avoidance and shortest safe path from source to the target.

Self-Organization and Autonomy in Computational Networks:Agents-based Contractual Workflow Paradigm

We describe an agents-based contractual workflow paradigm for Self-organization and autonomy in computational networks. The agent-based paradigm can be interpreted as the outcome arising out of deterministic, nondeterministic or stochastic interaction among a set of agents that includes the environment. These interactions are like chemical reactions and result in self-organization. Since the reaction rules are inherently parallel, any number of actions can be performed cooperatively or competitively among the subsets of elements, so that the agents carry out the required actions. Also we describe the application of this paradigm in finding short duration paths, chemical- patent mining, and in cloud computing services.

Reliable shortest path finding in stochastic networks with spatial correlated link travel times

This article proposes an efficient solution algorithm to aid travelers' route choice decisions in road network with travel time uncertainty, in the context of advanced traveler information systems (ATIS). In this article, the travel time of a link is assumed to be spatially correlated only to the neighboring links within a local ‘impact area.’ Based on this assumption, the spatially dependent reliable shortest path problem (SD-RSPP) is formulated as a multicriteria shortest path-finding problem. The dominant conditions for the SD-RSPP are established in this article. A new multicriteria A* algorithm is proposed to solve the SD-RSPP in an equivalent two-level hierarchical network. A case study using real-world data shows that link travel times are, indeed, only strongly correlated within the local impact areas; and the proposed limited spatial dependence assumption can well approximate path travel time variance when the size of the impact area is sufficiently large. Computational results demonstrate that the size of the impact area would have a significant impact on both accuracy and computational performance of the proposed solution algorithm.

Finding shortest path in static networks

This paper considers the problem of finding the shortest path in a static network, where the costs are constant. The CE Algorithm based strategy that is presented by Rubinstein to solving rare event and combinatorial optimization problem is modified to finding shortest path in this research. To analyze the efficiency of the used algorithm three sets of small, medium and large sized problems that generated randomly are solved. The results on the set of problems show that the modified algorithm produces good solutions and time saving in computation of large-scale network.

Analog Based Routing Algorithm using Ant Agents for MANETs (ABRAAM)

A mobile ad hoc network (MANET) is an anthology of wireless mobile hosts forming a short-lived network without the help of any centralized infrastructure. In such an environment, the reliable and shortest path finding between two hosts to transfer the payload is an extremely challenging task. The absence of a centralized infrastructure is a big problem in MANET where we cannot apply traditional routing algorithm used for standard wired networks. The three parameters tSignal Strength, Angle and Time of arrival are non-trivial parameters to decide the longevity and duration of a wireless link in a discovered route. A source node can analyze the reliability of a path and can establish an efficient routing algorithm for MANET by carefully measuring all analog measures and can predetermine the payload size which can be forwarded via that path.

A Fast Algorithm to Find All-Pairs Shortest Paths in Complex Networks

Finding shortest paths is a fundamental problem in graph theory, which has a large amount of applications in many areas like computer science, operations research, network routing and network analysis. Although many exact and approximate algorithms have been proposed, it is still a time-consuming task to calculate shortest paths for large-scale networks with tremendous volume of data available in recent years. In this paper, we find that the classic Dijkstra's algorithm can be improved by simple modification. We propose a fast algorithm which utilize the preiously-calculated results to accelerate the latter calculation. Simple optimization strategies are also proposed with consideration of characteristics of scale-free complex networks. Our experimental results show that the average running time of our algorithm is lower than the Dijkstra's algorithm by a factor relating to the connection probability in random networks of ER model. The performance of our algorithm is significantly better than the Dijkstra's algorithm in scale-free networks generated by the AB model. The results show that the time complexity is reduced to about O(n2.4) in scalefree complex networks. When the optimization strategies are applied, the algorithm performance is further improved slightly in scale-free networks.

The Analysis of Efficiency Dependence of the Shortest Path Finding Algorithms A* and HPA*

Many pathfinding problems in real-world applications require real-time computation of the shortest path between two points in a grid-based environment. It is not a trivial task. While some shortest path finding algorithms may perform admissibly in one condition, they may prove inadmissible in other conditions. HPA* pathfinding algorithm is faster and more memory efficient than the A*algorithm in relatively large two- dimensional grids, but this advantage may not apply to very small or very large grids. The paper deals with the efficiency of A* and HPA*in two-dimensional grids of different sizes. For the sake of completeness of the analysis, HPA* efficiency is measured taking into consideration the number of hierarchy levels and different cluster sizes. Both algorithms have been implemented and tests conducted. Experimental evidence is proposed to demonstrate the algorithm efficiency in various conditions.

Mobile robot path planning algorithm by equivalent conduction heat flow topology optimization

This paper addresses the path planning problem for a point robot moving in a planar environment filled with obstacles. Our approach is based on the principles of thermal conduction and structural topology optimization and rests on the observation that, by identifying the starting and ending configurations of a point robot as the heat source and sink of a conducting plate, respectively, the path planning problem can be formulated as a topology optimization problem that minimizes thermal compliance. Obstacles are modeled as regions of zero thermal conductivity; in fact, regions can be assigned varying levels of non-uniform conductivity depending on the application. We describe the details of our path planning algorithm, including the use of artificial mass constraints (particularly limits on the plate mass) to ensure convergence, and the choice of penalty exponents. The feasibility and practicality of our approach is validated through numerical experiments performed with several benchmarks, with intriguing possibilities for extension to more complex environments and real terrains. The benchmark problems of this paper mainly consist of obstacle-free path planning problems in two-dimensional space with maze-typed, symmetric, and spiral-type obstacles. We also address planning problems involving user-specified checkpoints, and also finding shortest paths on real three-dimensional terrain. To the authors' knowledge, the path planning going through a stopover is considered for the first time.

Efficient Energy-Optimal Routing for Electric Vehicles

Traditionally routing has focused on finding shortest paths in networks with positive, static edge costs representing the distance between two nodes. Energy-optimal routing for electric vehicles creates novel algorithmic challenges, as simply understanding edge costs as energy values and applying standard algorithms does not work. First, edge costs can be negative due to recuperation, excluding Dijkstra-like algorithms. Second, edge costs may depend on parameters such as vehicle weight only known at query time, ruling out existing preprocessing techniques. Third, considering battery capacity limitations implies that the cost of a path is no longer just the sum of its edge costs. This paper shows how these challenges can be met within the framework of A* search. We show how the specific domain gives rise to a consistent heuristic function yielding an O(n2) routing algorithm. Moreover, we show how battery constraints can be treated by dynamically adapting edge costs and hence can be handled in the same way as parameters given at query time, without increasing run-time complexity. Experimental results with real road networks and vehicle data demonstrate the advantages of our solution.

Shortest Path Problem in Stochastic Time-varying Transportation Networks Considering Risk Measurement

Stochastic, time-varying networks are proved a better tool in modeling transportation networks. In real transportation networks, routing policies often rely on shortest path, and finding shortest path is also proved a NP problem in STV networks. This paper presents a novel shortest path model based on expectation disutility function. The function portrays its risk measurement. In order to decrease the complexity of computation, the paper devises an approximation method in describing the path travel times. The method computes the travel time according to its distribution of arriving time of each node in the path. Compared to known methods, the approximation method prevents uncertain nesting computation coming from recursive formula, which is time-consuming in the face of large scale networks. Theoretical analysis and numerical example prove its efficiency and feasibility.

Partially Precomputed A$^{\ast}$

A* is a commonly used technique for finding shortest paths for navigation in video games. We propose partially precomputed A* (PPA*), which is much faster than A* at runtime, and uses much less memory than completely precalculating all shortest paths with an algorithm such as Floyd-Warshall. At runtime, PPA* is very similar to A*, so it is simple and safe to integrate into existing video game code bases.

Virtual network embedding through topology-aware node ranking

Virtualizing and sharing networked resources have become a growing trend that reshapes the computing and networking architectures. Embedding multiple virtual networks (VNs) on a shared substrate is a challenging problem on cloud computing platforms and large-scale sliceable network testbeds. In this paper we apply the Markov Random Walk (RW) model to rank a network node based on its resource and topological attributes. This novel topology-aware node ranking measure reflects the relative importance of the node. Using node ranking we devise two VN embedding algorithms. The first algorithm maps virtual nodes to substrate nodes according to their ranks, then embeds the virtual links between the mapped nodes by finding shortest paths with unsplittable paths and solving the multi-commodity flow problem with splittable paths. The second algorithm is a backtracking VN embedding algorithm based on breadth-first search, which embeds the virtual nodes and links during the same stage using node ranks. Extensive simulation experiments show that the topology-aware node rank is a better resource measure and the proposed RW-based algorithms increase the long-term average revenue and acceptance ratio compared to the existing embedding algorithms.

Self-organized cooperation between robotic swarms

We study self-organized cooperation between heterogeneous robotic swarms. The robots of each swarm play distinct roles based on their different characteristics. We investigate how the use of simple local interactions between the robots of the different swarms can let the swarms cooperate in order to solve complex tasks. We focus on an indoor navigation task, in which we use a swarm of wheeled robots, called foot-bots, and a swarm of flying robots that can attach to the ceiling, called eye-bots. The task of the foot-bots is to move back and forth between a source and a target location. The role of the eye-bots is to guide foot-bots: they choose positions at the ceiling and from there give local directional instructions to foot-bots passing by. To obtain efficient paths for foot-bot navigation, eye-bots need on the one hand to choose good positions and on the other hand learn the right instructions to give. We investigate each of these aspects. Our solution is based on a process of mutual adaptation, in which foot-bots execute instructions given by eye-bots, and eye-bots observe the behavior of foot-bots to adapt their position and the instructions they give. Our approach is inspired by pheromone mediated navigation of ants, as eye-bots serve as stigmergic markers for foot-bot navigation. Through simulation, we show how this system is able to find efficient paths in complex environments, and to display different kinds of complex and scalable self-organized behaviors, such as shortest path finding and automatic traffic spreading.

Query Processing Using Distance Oracles for Spatial Networks

The popularity of location-based services and the need to do real-time processing on them has led to an interest in performing queries on transportation networks, such finding shortest paths and finding nearest neighbors. The challenge here is that the efficient execution of spatial operations usually involves the computation of distance along a spatial network instead of as the crow flies, which is not simple. Techniques are described that enable the determination of the network distance between any pair of points (i.e., vertices) with little O(n) space rather than having to store the n2 distances between all pairs. This is done by being willing to expend a bit more time to achieve this goal such O(log n) instead of O(1), well by accepting an error e in the accuracy of the distance that is provided. The strategy that is adopted reduces the space requirements and is based on the ability to identify groups of source and destination vertices for which the distance is approximately the same within some e. The reductions are achieved by introducing a construct termed a distance oracle that yields an estimate of the network distance (termed the e-approximate distance) between any two vertices in the spatial network. The distance oracle is obtained by showing how to adapt the well-separated pair technique from computational geometry to spatial networks. Initially, an e-approximate distance oracle of size O(n/(e2)) is used that is capable of retrieving the approximate network distance in O(log n) time using a B-tree. The retrieval time can be theoretically reduced further to O(1) time by proposing another e-approximate distance oracle of size O((n log n)/(e2)) that uses a hash table. Experimental results indicate that the proposed technique is scalable and can be applied to sufficiently large road networks. For example, a 10-percentapproximate oracle (e = 0.1) on a large network yielded an average error of 0.9 percent with 90 percent of the answers having an error of 2 percent or less and an average retrieval time of 68 μ seconds. The fact that the network distance can be approximated by one value is used to show how a number of spatial queries can be formulated using appropriate SQL constructs and a few built-in primitives. The result is that these operations can be executed on almost any modern database with no modifications, while taking advantage of the existing query optimizers and query processing strategies.