A Study on Time-Dependent Reachability and Route Scheduling in Road Network

Abstract

For thousands of years, humans have been innovating new technologies to plan their journeys: from looking up the starry sky, to depending on the magnetic compass; from referring to precious ancient maps, to interacting with locals for nearby information. However, these approaches are either inaccurate or hard to grasp by ordinary people. Thanks to the recent rapid development of online map services and GPS devices, we are able to identify where we are on earth, find any place we want to go, and retrieve a route to it. Although it is convenient and fast enough for basic uses, it is still far from optimal. For starters, most systems just provide a shortest path without considering the traffic condition. Secondly, some systems consider the current traffic condition to provide an estimated travel time. However, the lack of estimation for future traffic condition cannot help us plan the travel ahead of time. To make the things worse, the computation that takes traffic condition into consideration grows slower as the planning time interval and the distance grow longer. Therefore, we study how to plan a travel that considers traffic information from the following aspects. The first one is the reachability problem. A road network, or a map, is essentially a graph with nodes representing intersections and edges representing roads. For a well-maintained map, the nodes are reachable to each other. However, this is not always the case when we obtain our map data. For example, the nodes along the boundary might not reach the other nodes on the map. We propose a High-Dimensional Graph Dominance Drawing approach to answer if one node can reach another quickly on large graphs. In fact, it takes only constant time to answer reachability query in road network. We run our algorithm on various of graph structures with different configurations to fully test its performance. The results help us have a deeper understanding on the reachability problem. The second one is the speed profile generation. A speed profile is a set of functions that return the travel time of any road by providing any departure time. Many existing works just assume such a speed profile exists, or generate one synthetically. Other real-life applications tend to use real-time data from sensors monitoring major roads, which is expensive to deploy and unable to cover a large area. In this work, we use historical trajectories of taxis to generate a speed profile. It involves map-matching, speed data collecting, missing value estimation and compression. By using different speed profile for different types of day, we can provide route scheduling that satisfying user's need. Extensive experiments show that our speed profile is accurate and space efficient. The third one is the minimal on-road travel time route scheduling (MORT). This is a general form of all the single criteria path problems. All the existing path finding problem does not allow iii waiting on some vertices along the route, nor can they benefit from it. We extend this problem by allowing waiting. In this...