Applications of graph algorithms in GIS

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Generalized Maneuvers in Route Planning for Computing and Informatics

We study an important practical aspect of the route planning problem in real-world road networks -- maneuvers. Informally, maneuvers represent various irregularities of the road network graph such as turn-prohibitions, traffic light delays, round-abouts, forbidden passages and so on. We propose a generalized model which can handle arbitrarily complex (and even negative) maneuvers and extend traditional Dijkstra's Algorithm in order to solve route planning queries in this model without prior adjustments of the underlying road network graph. Finally, we also briefly evaluate practical performance of our approach (as compared to ordinary Dijkstra on an amplified network graph)

3D oceanographic data compression using 3D-ODETLAP

This paper describes a 3D environmental data compression technique for oceanographic datasets. With proper point selection, our method approximates uncompressed marine data using an over-determined system of linear equations based on, but essentially different from, the Laplacian partial differential equation. Then this approximation is refined via an error metric. These two steps work alternatively until a predefined satisfying approximation is found. Using several different datasets and metrics, we demonstrate that our method has an excellent compression ratio. To further evaluate our method, we compare it with 3D-SPIHT. 3D-ODETLAP averages 20% better compression than 3D-SPIHT on our eight test datasets, from World Ocean Atlas 2005. Our method provides up to approximately six times better compression on datasets with relatively small variance. Meanwhile, with the same approximate mean error, we demonstrate a significantly smaller maximum error compared to 3D-SPIHT and provide a feature to keep the maximum error under a user-defined limit

Optimal ship navigation and algorithms for stochactic obstacle scenes

Tezin basılısı İstanbul Şehir Üniversitesi Kütüphanesi'ndedir.This thesis is comprised of two different but related sections. In the first section, we consider the optimal ship navigation problem wherein the goal is to find the shortest path between two given coordinates in the presence of obstacles subject to safety distance and turn-radius constraints. These obstacles can be debris, rock formations, small islands, ice blocks, other ships, or even an entire coastline. We present a graph-theoretic solution on an appropriately-weighted directed graph representation of the navigation area obtained via 8-adjacency integer lattice discretization and utilization of the A∗ algorithm. We explicitly account for the following three conditions as part of the turn-radius constraints: (1) the ship’s left and right turn radii are different, (2) ship’s speed reduces while turning, and (3) the ship needs to navigate a certain minimum number of lattice edges along a straight line before making any turns. The last constraint ensures that the navigation area can be discretized at any desired resolution. We illustrate our methodology on an ice navigation example involving a 100,000 DWT merchant ship and present a proof- of-concept by simulating the ship’s path in a full-mission ship handling simulator at Istanbul Technical University. In the second section, we consider the stochastic obstacle scene problem wherein an agent needs to traverse a spatial arrangement of possible-obstacles, and the status of the obstacles may be disambiguated en route at a cost. The goal is to find an algorithm that decides what and where to disambiguate en route so that the expected length of the traversal is minimized. We present a polynomial-time method for a graph-theoretical version of the problem when the associated graph is restricted to parallel avenues with fixed policies within the avenues. We show how previously proposed algorithms for the continuous space version can be adapted to a discrete setting. We propose a gener- alized framework encompassing these algorithms that uses penalty functions to guide the navigation in realtime. Within this framework, we introduce a new algorithm that provides near-optimal results within very short execution times. Our algorithms are illustrated via computational experiments involving synthetic data as well as an actual naval minefield data set. Keywords: Graph theory, shortest path, ship navigation, probabilistic path planning, stochastic dynamic programming, Markov decision process, Canadian traveler’s problemContents Declaration of Authorship ii Abstract iv ¨ Oz v Acknowledgments vii List of Figures x List of Tables xi 1 Optimal Ship Navigation with Safety Distance and Realistic Turn Con- straints 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 The Optimal Ship Navigation Problem . . . . . . . . . . . . . . . . . . . . 4 1.4 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4.1 Safety Distance Constraints . . . . . . . . . . . . . . . . . . . . . . 5 1.4.2 Lattice Discretization . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4.3 Ship-Turn Constraints . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4.4 The A∗ Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.4.5 Smoothing the Optimal Path . . . . . . . . . . . . . . . . . . . . . 13 1.5 Ice Navigation Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.6 Simulator Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.7 Summary, Conclusions, and Future Research . . . . . . . . . . . . . . . . 18 2 Algorithms for Stochastic Obstacle Scenes 21 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2 The Stochastic Obstacle Scene Problem: Continuous vs. Discrete Settings 23 2.2.1 Deciding Where to Disambiguate: Single Disk Case . . . . . . . . 23 2.2.2 Deciding Where to Disambiguate: Two Disks Case . . . . . . . . . 25 2.2.3 Discretization of the Continuous Setting: An Example . . . . . . . 27 2.3 Definition of the Stochastic Obstacle Scene Problem . . . . . . . . . . . . 27 2.3.1 Continuous SOSP . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.3.2 Discrete SOSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.3.3 Discretized SOSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.4 A Polynomial Algorithm for Discrete SOSP on Parallel Graphs . . . . . . 29 2.5 Discrete Adaptation of the Simulated Risk Disambiguation Algorithm . . 30 2.5.1 Adaptation to Discrete SOSP . . . . . . . . . . . . . . . . . . . . . 30 2.5.2 Adaptation to Discretized SOSP . . . . . . . . . . . . . . . . . . . 32 2.6 Discrete Adaptation of the Reset Disambiguation Algorithm . . . . . . . . 33 2.7 Generalizing SRA and RDA: Penalty-Based Algorithms and DTA . . . . . 34 2.7.1 Illustration of the Algorithms . . . . . . . . . . . . . . . . . . . . . 36 2.8 Computational Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.8.1 Environment A (The COBRA Data) Experiments . . . . . . . . . 40 2.8.2 Environment B Experiments . . . . . . . . . . . . . . . . . . . . . 41 2.8.3 Environment C Experiments . . . . . . . . . . . . . . . . . . . . . 43 2.9 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 A Impact of Cost Change in Parallel Graphs 47 Bibliograph

A Note on Hierarchical Routing Algorithms based on Traverse-oriented Road Networks

Finding the shortest route has become almost an omnipresent task in our society. This task runs across in the internet, for outdoor activities and of course within in-car navigation systems. Nowadays finding the shortest path gets more popular compared to the past because of rising fuel prices. That is why driving along an optimised route has financial benefits on the one hand and on the other hand it spares energy resources of our environment. In this paper a hierarchical approach of route computation based on traverse elements is discussed. Furthermore an experimental setup consisting of an open source database management system (PostgreSQL/PostGIS) is realised to verify the theoretical part

Applications

Volume 3 describes how resource-aware machine learning methods and techniques are used to successfully solve real-world problems. The book provides numerous specific application examples: in health and medicine for risk modelling, diagnosis, and treatment selection for diseases in electronics, steel production and milling for quality control during manufacturing processes in traffic, logistics for smart cities and for mobile communications

Applications

Volume 3 describes how resource-aware machine learning methods and techniques are used to successfully solve real-world problems. The book provides numerous specific application examples: in health and medicine for risk modelling, diagnosis, and treatment selection for diseases in electronics, steel production and milling for quality control during manufacturing processes in traffic, logistics for smart cities and for mobile communications