Statistics for Spatial Data.

Introduction to linear and nonlinear programming

In this chapter, you will see how the simplex method simplifies when it is applied to a class of optimization problems that are known as “network flow models.” You will also see that if a network flow model has “integer-valued data,” the simplex method finds an optimal solution that is integer-valued.

Flows in Networks

The power of any kind of network approach lies in the ability to simplify a complex system so that one can better understand its function as a whole. Sometimes it is beneficial, however, to include more information than in a simple graph of only nodes and links. Adding information about times of interactions can make predictions and mechanistic understanding more accurate. The drawback, however, is that there are not so many methods available, partly because temporal networks is a relatively young field, partly because it is more difficult to develop such methods compared to for static networks. In this colloquium, we review the methods to analyze and model temporal networks and processes taking place on them, focusing mainly on the last three years. This includes the spreading of infectious disease, opinions, rumors, in social networks; information packets in computer networks; various types of signaling in biology, and more. We also discuss future directions.

/pdf/modern-temporal-network-theory-a-colloquium-2artviu6zb.pdf

Modern temporal network theory: a colloquium

The power of any kind of network approach lies in the ability to simplify a complex system so that one can better understand its function as a whole. Sometimes it is beneficial, however, to include more information than in a simple graph of only nodes and links. Adding information about times of interactions can make predictions and mechanistic understanding more accurate. The drawback, however, is that there are not so many methods available, partly because temporal networks is a relatively young field, partly because it more difficult to develop such methods compared to for static networks. In this colloquium, we review the methods to analyze and model temporal networks and processes taking place on them, focusing mainly on the last three years. This includes the spreading of infectious disease, opinions, rumors, in social networks; information packets in computer networks; various types of signaling in biology, and more. We also discuss future directions.

Modern temporal network theory: A colloquium

Evacuation planning is critical for numerous important applications, e.g. disaster emergency management and homeland defense preparation. Efficient tools are needed to produce evacuation plans that identify routes and schedules to evacuate affected populations to safety in the event of natural disasters or terrorist attacks. The existing linear programming approach uses time-expanded networks to compute the optimal evacuation plan and requires a user-provided upper bound on evacuation time. It suffers from high computational cost and may not scale up to large transportation networks in urban scenarios. In this paper we present a heuristic algorithm, namely Capacity Constrained Route Planner(CCRP), which produces sub-optimal solution for the evacuation planning problem. CCRP models capacity as a time series and uses a capacity constrained routing approach to incorporate route capacity constraints. It addresses the limitations of linear programming approach by using only the original evacuation network and it does not require prior knowledge of evacuation time. Performance evaluation on various network configurations shows that the CCRP algorithm produces high quality solutions, and significantly reduces the computational cost compared to linear programming approach that produces optimal solutions. CCRP is also scalable to the number of evacuees and the size of the network.

/pdf/capacity-constrained-routing-algorithms-for-evacuation-367diwfcia.pdf

Capacity constrained routing algorithms for evacuation planning: a summary of results

Spatio-temporal networks are spatial networks whose topology and parameters change with time. These networks are important due to many critical applications such as emergency traffic planning and route finding services and there is an immediate need for models that support the design of efficient algorithms for computing the frequent queries on such networks. This problem is challenging due to potentially conflicting requirements of model simplicity and support for efficient algorithms. Time expanded networks which have been used to model dynamic networks employ replication of the network across time instants, resulting in high storage overhead and algorithms that are computationally expensive. In contrast, proposed time-aggregated graphs do not replicate nodes and edges across time; rather they allow the properties of edges and nodes to be modeled as a time series. Since the model does not replicate the entire graph for every instant of time, it uses less memory and the algorithms for common operations (e.g. connectivity, shortest path) are computationally more efficient than those for time expanded networks. One important query on spatio-temporal networks is the computation of shortest paths. Shortest paths can be computed either for a given start time or to find the start time and the path that leads to least travel time journeys (best start time journeys). Developing efficient algorithms for computing shortest paths in a time varying spatial network is challenging because these journeys do not always display greedy property or optimal substructure, making techniques like dynamic programming inapplicable. In this paper, we propose algorithms for shortest path computations in both contexts. We present the analytical cost models for the algorithms and provide an experimental comparison of performance with existing algorithms.

Spatio-temporal network databases and routing algorithms: a summary of results

Given a transportation network, a vulnerable population, and a set of destinations, evacuation route planning identifies routes to minimize the time to evacuate the vulnerable population. Evacuation route planning is a vital components of efforts by civil authorities to prepare for both natural and man-made disasters (e.g., hurricanes, terrorist acts, etc). However, evacuation route planning is computationally challenging due to the size of transportation networks, the large number of evacuees, and capacity constraints. For example, the number of evacuees often far exceeds the bottleneck capacity, i.e., the minimum cut of a given network. Current approaches (e.g., linear programming and Capacity Constrained Route Planner (CCRP), a recently proposed evacuation planning algorithm) do not scale well because of intensive computation needs in order to produce the schedules of evacuees as well as routing plans.This paper presents innovative heuristics scalable to very large transportation networks. The Intelligent Load Reduction heuristic accelerates the routing computation by the reduction of evacuees using the bottleneck saturation. The performance of Intelligent Load Reduction is evaluated using real world scenarios. Results show that the Intelligent Load Reduction heuristic significantly improve the runtime of CCRP. We propose another heuristic named Incremental Data Structure. While the Intelligent Load Reduction gains performance increase by giving up the schedules of evacuees, the Incremental Data Structure heuristic can reduce calculation time of the CCRP algorithm by the enhanced data structures without affecting the outputs.

Evacuation route planning: scalable heuristics

Efficient tools are needed to identify routes and schedules to evacuate affected populations to safety in the event of natural disasters. Hurricane Rita and the recent tsunami revealed limitations of traditional approaches to provide emergency preparedness for evacuees and to predict the effects of evacuation route planning ERP. Challenges arise during evacuations due to the spread of people over space and time and the multiple paths that can be taken to reach them; key assumptions such as stationary ranking of alternative routes and optimal substructure are violated in such situations. Algorithms for ERP were first developed by researchers in operations research and transportation science. However, these proved to have high computational complexity and did not scale well to large problems. Over the last decade, we developed a different approach, namely the Capacity Constrained Route Planner CCRP, which generalizes shortest path algorithms by honoring capacity constraints and the spread of people over space and time. The CCRP uses time-aggregated graphs to reduce storage overhead and increase computational efficiency. Experimental evaluation and field use in Twin Cities Homeland Security scenarios demonstrated that CCRP is faster, more scalable, and easier to use than previous techniques. We also propose a novel scalable algorithm that exploits the spatial structure of transportation networks to accelerate routing algorithms for large network datasets. We evaluated our new approach for large-scale networks around downtown Minneapolis and riverside areas. This article summarizes experiences and lessons learned during the last decade in ERP and relates these to Professor Goodchild's contributions.

Experiences with evacuation route planning algorithms

Given applications such as location based services and the spatio-temporal queries they may pose on a spatial network (e.g., road networks), the goal is to develop a simple and expressive model that honors the time dependence of the road network. The model must support the design of efficient algorithms for computing the frequent queries on the network. This problem is challenging due to potentially conflicting requirements of model simplicity and support for efficient algorithms. Time expanded networks, which have been used to model dynamic networks employ replication of the networks across time instants, resulting in high storage overhead and algorithms that are computationally expensive. In contrast, the proposed time-aggregated graphs do not replicate nodes and edges across time; rather they allow the properties of edges and nodes to be modeled as a time series. Since the model does not replicate the entire graph for every instant of time, it uses less memory and the algorithms for common operations are computationally more efficient than for time expanded networks. One important query on spatio-temporal networks is the computation of shortest paths. Shortest paths can be computed either for a given start time or to find the start time and the path that lead to least travel time journeys (best start time journeys). Developing efficient algorithms for computing shortest paths in a time variant spatial network is challenging because these journeys do not always display optimal prefix property, making techniques like dynamic programming inapplicable. In this paper, we propose algorithms for shortest path computation for a fixed start time. We present the analytical cost model for the algorithm and compare with the performance of existing algorithms.

Betsy George

Papers

Capacity constrained routing algorithms for evacuation planning: a summary of results

Spatio-temporal network databases and routing algorithms: a summary of results

Evacuation route planning: scalable heuristics

Experiences with evacuation route planning algorithms

Time-Aggregated Graphs for Modeling Spatio-temporal Networks