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.

The Value of Waiting: Foreign Direct Investment with Uncertainty and Imperfect Local Knowledge

This paper examines the role of uncertainty and imperfect local knowledge in foreign direct investment. The main idea comes from the literature on investment under uncertainty, such as Pindyck (1991) and Dixit and Pindyck (1994). We empirically test .the value of waiting. with a dataset on foreign direct investment (FDI). Many factors (e.g., political and economic regulations) as well as uncertainty and the risks due to imperfect local knowledge, determine the attractiveness of FDI. The uncertainty and irreversibility of FDI links the time interval between permission and actual execution of such FDI with explanatory variables, including information on foreign (home) countries and domestic industries. Common factors, such as regulatory change and external shocks, may affect the uncertainty when foreign investors make irreversible FDI decisions. We derive testable hypotheses from models of investment under uncertainty to determine those possible factors that induce delays in FDI, using Korean data over 1962 to 2001.