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 waiting on some vertices along the route, nor can they benefit from it. We extend this problem by allowing waiting. In this way, the total travel time is made up of two parts: on-road travel time and waiting time. Now we are able to find a route with minimum on-road time. Such query is needed by logistics company and tourists. The challenging part of the routing problem lies in the computational complexity when determining if it is beneficial to wait on specifying the parking places and the corresponding time of waiting to maximize the benefit. To cope with this challenging problem, we propose two efficient algorithms using minimum on-road travel cost function to answer the query. We further introduce several approximation methods to speed up the query answering. Experiments show that our method is more efficient and accurate than baseline approaches extended from the existing path planning algorithms.The last one the time-dependent 2-hop labeling. The time-dependent path algorithms are still slow because the fastest path problem's complexity is Ω(T(|V|\log|V|+|E|)), where T is the number of turning points in the result's function and it is large in real-life query. Therefore, we extend the 2-Hop labeling index to time-dependent environment. Besides, our approach can also answer time-dependent reachability query. However, even for a static graph, the label size is already at least Ω(|V||E|1/2), so it would be much bigger if we extend it directly. So we propose a partition-based framework to adapt to the real-life road network. By breaking the query into three parallel parts, we are able to speed up any time-dependent query for thousands of times. To further reduce the label size and speed up query answering, we propose an approximation approach with the worst case error bounded. Comparison with the existing on-line search indexes shows that our time-dependent 2-hop can answer queries much faster, with an acceptable index size.