Fast Algorithms Using Minimal Data Structures for Common Topological Relationships in Large, Irregularly-spaced Topographic Data Sets

Digital terrain models (DTM) typically contain large numbers of postings, from hundreds of thousands to billions. Many algorithms that run on DTMs require topological knowledge of the postings, such as finding nearest neighbors, finding the posting closest to a chosen location, etc. If the postings are arranged irregu- larly, topological information is costly to compute and to store. This paper offers a practical approach to organizing and searching irregularly-space data sets by presenting a collection of efficient algorithms (O(N),O(lgN)) that compute important topological relationships with only a simple supporting data structure. These relationships include finding the postings within a window, locating the posting nearest a point of interest, finding the neighborhood of postings nearest a point of interest, and ordering the neighborhood counter-clockwise. These algorithms depend only on two sorted arrays of two-element tuples, holding a planimetric coordinate and an integer identification number indicating which posting the coordinate belongs to. There is one array for each planimetric coordinate (eastings and northings). These two arrays cost minimal overhead to create and store but permit the data to remain arranged irregularly.

Forecasting and Analyzing Economic Activity with Coincident and Leading Indexes: The Case of Connecticut

We develop coincident and leading employment indexes for the Connecticut economy. Four employment-related variables enter the coincident index while five employment-related variables enter the leading index. The peaks and troughs in the leading index lead the peaks and troughs in the coincident index by an average of 3 and 9 months. Finally, we use the leading index in vector-autoregressive (VAR) and Bayesian vector-autoregressive (BVAR) models to forecast the coincident index, nonfarm employment, and the unemployment rate.