A generic triangle-based data structure of the complete set of higher order Voronoi diagrams for emergency management

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Abstract

We introduce a generic Delaunay triangle-based data structure for geoinformation processing in disaster and emergency management. The data structure supports the complete set of higher order Voronoi diagrams (order-k) Voronoi diagrams, ordered order-k Voronoi diagrams, and k-th nearest Voronoi diagrams for all (k). It provides useful and insightful information for what-if nearest queries, what-if neighboring queries, what-if zoning queries, what-if facility locating queries and what-if routing queries to handle various scenarios in the four stages of emergency management (mitigation, preparedness, response and recovery). We also demonstrate how the complete set of higher order Voronoi diagrams can be used for each phase of emergency management in diverse geoinformatics environments.

Introduction

Sensors monitoring regions of interest are continuously producing geospatial data for disaster analysis and emergency management. The ubiquitous data collection requires dynamic geoinformation processing for real-time emergency analysis and management. Disasters and emergencies are detrimental to people, property and environment. Real-time analysis and management of emergencies is of great importance as the lack of appropriate emergency management could lead to environmental damage, financial and structural losses or destruction of civilian infrastructure. This has become increasingly important in a time of escalating emergency situations resulting from terrorist attacks and the effects of global warming. Intelligent processing of geoinformation for emergency management is in high demand to assist with the protection of people, property and the environment from these types of emergencies.

GIS (Geographic Information Systems) providing data acquisition, interpretation and dissemination are essential in most aspects of natural disaster and emergency management (Goodchild, 2006). GIS provide a centralized mechanism to visually display emergency information (Johnson, 1994), and they have been used by many initiatives and researchers for hazard and disaster decision support (Chang et al., 1997, Dymon and Winter, 1993, Kevany, 2003, Montoya, 2003, Salt and Dunsmore, 2000). However, much of the research is limited to producing cartographic mappings and visualization rather than disaster analysis and predictive modeling (Zerger & Smith, 2003). Particularly in emergency management, (1) ordered and unordered geometric k-nearest queries (returning geometrically k nearest neighbors), (2) kth-order topological neighboring queries (returning k-th-order topological neighboring regions), (3) k-nearest zoning (districting) queries, (4) facility locating queries, and (5) routing queries are of great importance. Currently GIS do not systemically support all of these queries simultaneously, and also lack a generic data structure supporting all these queries for “what-if” analysis in highly dynamic environments.

Geospatial tessellations attempt to answer some of these queries by segmenting the space into meaningful sub-regions (districts) (Okabe, Boots, Sugihara, & Chiu, 2000). For instance, they have been used in market area analysis and spatial competition (Hanjoul et al., 1989, Okabe et al., 2000, Rushton and Thill, 1989, Thill and Rushton, 1992). Hanjoul et al. (1989) investigated the boundaries of market areas by tessellating the space into regions of dominance in the Euclidean space. Rushton and Thill, 1989, Thill and Rushton, 1992 further compared spatial competition and the boundaries of market areas in the Euclidean space against the Manhattan space. However, these studies are limited to order-1 (dominant region of one city) and are not able to model higher order dominant regions such as a dominant region of four cities (order-4). In addition, these studies theoretically model the boundaries of market areas, but do not provide a data structure for practical implementation. The Voronoi diagram and its dual Delaunay triangulation offer a robust framework for modeling and structuring geospatial tessellations (Okabe et al., 2000). They are used for what-if analysis in a wide spectrum of geosciences and environmental sciences (Okabe et al., 2000). Higher order Voronoi diagrams, popular generalizations of the Voronoi diagram, provide informative insights into the generalized what-if queries suggested previously. Despite the popularity of higher order Voronoi diagrams, we still lack a generic unified data structure to support them.

This paper introduces a generic Delaunay triangle-based data structure for geoinformation processing in disaster and emergency management. For a given set of n generators, this data structure encompasses the complete set of higher order Voronoi diagrams (referred to as the complete higher order Voronoi diagrams) providing useful information for nearest, neighboring, zoning, locating and routing queries to handle various scenarios in the four stages of emergency management (mitigation, preparedness, response, and recovery).

The complete higher order Voronoi diagrams are all order-k, ordered order-k Voronoi diagrams, and k-th nearest Voronoi diagrams for k=1,,n-1. The framework builds a unified order-k Delaunay triangle data structure from which users can derive the complete higher order Voronoi diagrams for various emergency scenarios to support various what-if scenarios. Building the generic data structure requires O(n4) time, and once it is determined computing the complete higher order Voronoi diagrams requires O(n3logn) time. In this article, the unified data structure is limited to the Euclidean space where “crow flies distance” applies. This is of particular use in large scale analysis, and marine or aerial environments where a straight line between two targets makes sense.

Section snippets

Background

Given a set P={p1,p2,,pn} of distinct generators, the ordinary Voronoi diagram is obtained by assigning all locations in the space to the closest generator. Locations equidistant from two generators form Voronoi edges while locations equidistant from more than two generators constitute Voronoi vertices. This assignment tessellates the space into mutually exclusive and collectively exhaustive Voronoi regions. Higher order Voronoi diagrams (order-k, ordered order-k, and k-th nearest Voronoi

Emergency management with higher order Voronoi diagrams

Emergency management is composed of four basic phases: mitigation, preparedness, response, and recovery (Haddow & Bullock, 2003). This section demonstrates how the complete higher order Voronoi diagrams can be used for each stage of emergency management. We explain this with a study region S of Townsville, a tropical city of northern Queensland in Australia. The study region consists of 42 urban suburbs of Townsville and suffers from periodic tropical cyclones accompanying strong winds and

Summary and future work

Disasters and emergency situations can lead to various forms of financial, structural and environmental damage. Even though it is almost impossible to avoid occurrences of disasters, effective prediction and preparedness along with an post emergency management program can mitigate the risk and damage (Jayaraman, Chandrasekhar, & Rao, 1997). What-if ordered and unordered k-nearest point queries, kth-neighboring queries, districting, facility locating queries and routing queries are therefore of

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