Algorithms for advanced path optimization problems

With the ever-increasing popularity of smart phones appended with a Global Positioning System (GPS), people tend to use GPS-based applications to assist them in reaching their destinations. Different people can have different optimization criteria in path finding. This thesis contributes into improving the current navigation systems by studying and solving three new path finding problems. Finding Lowest-Cost Paths in Settings with Safe and Preferred Zones Problem: Given a set of safe or preferred zones with zero or low cost, this problem finds paths that minimize the cost of travel from an origin to a destination. A life-critical application of this problem is navigating through scattered populated areas (safe zones) in hazardous environments such as deserts. In a more familiar scenario, a tourist who plans to walk to a given destination may prefer a path that visits interesting streets and blocks, e.g., with interesting houses, galleries, or other sights, (proffered zones) as much as possible. We solved this problem by proposing an algorithm that utilizes the properties of hyperbolas to elegantly describe a sparsely connected safe (preferred) zones graph. Skyline Trips of Multiple POIs Categories Problem: Given a road network with a set of Points of Interest (POIs) from different categories, a list of items the user is planning to purchase and a pricing function for items at each related POI, this problem finds the skyline trips in terms of both trip length and trip aggregated cost. This problem has important applications in everyday life. Specifically, it helps people choose the most suitable trips among the skyline trips based on two dimensions: trip total length and trip aggregated cost. We proposed a framework and two effective algorithms to efficiently solve the problem in real time which produce near optimal results when tested on real datasets.