Finding the shortest paths in a graph has been studied for a long time, and there are many main memory based algorithms dealing with this problem. Among these, Dijkstra's shortest path algorithm is one of the most commonly used efficient algorithms to the non-negative graphs. Even more efficient algorithms have been developed recently for graphs with particular properties such as the weights of edges fall into a range of integer. All of the mentioned algorithms require the graph totally reside in the main memory. Howevery, for very large graphs, such as the digital maps managed by Geographic Information Systems (GIS), the requirement cannot be satisfied in most cases, so the algorithms mentioned above are not appropriate. My objective in this thesis is to design and evaluate the performance of external memory (disk-based) shortest path algorithms and data structures to solve the shortest path problem in very large digital maps. In particular the following questions are studied:What have other researchers done on the shortest path queries in very large digital maps?What could be improved on the previous works? How efficient are our new shortest paths algorithms on the digital maps, and what factors affect the efficiency? What can be done based on the algorithm? In this thesis, we give a disk-based Dijkstra's-like algorithm to answer shortest path queries based on pre-processing information. Experiments based on our Java implementation are given to show what factors affect the running time of our algorithms.

Distributed-system observation is foundational to understanding and controlling distributed computations. Existing tools for distributed-system observation are constrained in the size of computation that they can observe by three fundamental problems. They lack scalable information collection, scalable data-structures for storing and querying the information collected, and scalable information-abstraction schemes. This dissertation addresses the second of these problems. Two core problems were identified in providing a scalable data structure. First, in spite of the existence of several distributed-system-observation tools, the requirements of such a structure were not well-defined. Rather, current tools appear to be built on the basis of events as the core data structure. Events were assigned logical timestamps, typically Fidge/Mattern, as needed to capture causality. Algorithms then took advantage of additional properties of these timestamps that are not explicit in the formal semantics. This dissertation defines the data-structure interface precisely, and goes some way toward reworking algorithms in terms of that interface. The second problem is providing an efficient, scalable implementation for the defined data structure. The key issue in solving this is to provide a scalable precedence-test operation. Current tools use the Fidge/Mattern timestamp for this. While this provides a constant-time test, it requires space per event equal to the number of processes. As the number of processes increases, the space consumption becomes sufficient to affect the precedence-test time because of caching effects. It also becomes problematic when the timestamps need to be copied between processes or written to a file. Worse, existing theory suggested that the space-consumption requirement of Fidge/Mattern timestamps was optimal. In this dissertation we present two alternate timestamp algorithms that require substantially less space than does the Fidge/Mattern algorithm.

Distributed-system observation is foundational to understanding and controlling distributed computations. Existing tools for distributed-system observation are constrained in the size of computation that they can observe by three fundamental problems. They lack scalable information collection, scalable data-structures for storing and querying the information collected, and scalable information-abstraction schemes. This dissertation addresses the second of these problems. Two core problems were identified in providing a scalable data structure. First, in spite of the existence of several distributed-system-observation tools, the requirements of such a structure were not well-defined. Rather, current tools appear to be built on the basis of events as the core data structure. Events were assigned logical timestamps, typically Fidge/Mattern, as needed to capture causality. Algorithms then took advantage of additional properties of these timestamps that are not explicit in the formal semantics. This dissertation defines the data-structure interface precisely, and goes some way toward reworking algorithms in terms of that interface. The second problem is providing an efficient, scalable implementation for the defined data structure. The key issue in solving this is to provide a scalable precedence-test operation. Current tools use the Fidge/Mattern timestamp for this. While this provides a constant-time test, it requires space per event equal to the number of processes. As the number of processes increases, the space consumption becomes sufficient to affect the precedence-test time because of caching effects. It also becomes problematic when the timestamps need to be copied between processes or written to a file. Worse, existing theory suggested that the space-consumption requirement of Fidge/Mattern timestamps was optimal. In this dissertation we present two alternate timestamp algorithms that require substantially less space than does the Fidge/Mattern algorithm.

Finding the shortest paths in a graph has been studied for a long time, and there are many main memory based algorithms dealing with this problem. Among these, Dijkstra's shortest path algorithm is one of the most commonly used efficient algorithms to the non-negative graphs. Even more efficient algorithms have been developed recently for graphs with particular properties such as the weights of edges fall into a range of integer. All of the mentioned algorithms require the graph totally reside in the main memory. Howevery, for very large graphs, such as the digital maps managed by Geographic Information Systems (GIS), the requirement cannot be satisfied in most cases, so the algorithms mentioned above are not appropriate. My objective in this thesis is to design and evaluate the performance of external memory (disk-based) shortest path algorithms and data structures to solve the shortest path problem in very large digital maps. In particular the following questions are studied:What have other researchers done on the shortest path queries in very large digital maps?What could be improved on the previous works? How efficient are our new shortest paths algorithms on the digital maps, and what factors affect the efficiency? What can be done based on the algorithm? In this thesis, we give a disk-based Dijkstra's-like algorithm to answer shortest path queries based on pre-processing information. Experiments based on our Java implementation are given to show what factors affect the running time of our algorithms.