Suppose a company wants to design a data warehouse to facilitate the analysis of moving vehicles in an online analytical processing manner. The company registers huge amounts of auto movement data in the format of (Auto ID, location, speed, time). Each Auto ID represents a vehicle associated with information (e.g., vehicle category, driver category), and each location may be associated with a street in a city. Assume that a street map is available for the city.

(a) Design such a data warehouse to facilitate effective online analytical processing in multidimensional space.

(b) The movement data may contain noise. Discuss how you would develop a method to automatically discover data records that were likely erroneously registered in the data repository.

(c) The movement data may be sparse. Discuss how you would develop a method that constructs a reliable data warehouse despite the sparsity of data.

(d) If you want to drive from A to B starting at a particular time, discuss how a system may use the data in this warehouse to work out a fast route.