Route Planning in Transportation Networks (1504.05140v1)

Abstract: We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.

• The paper demonstrates that advanced techniques like Contraction Hierarchies, Transit Node Routing, and RAPTOR achieve rapid query responses and scalability in various network models.
• It highlights robust methodologies for static, dynamic, and time-dependent routing that address complexities in both road and public transit systems.
• The study underscores the need for integrating real-time data and personalization to enhance multimodal journey planning and overall routing efficiency.

Route Planning in Transportation Networks

The paper "Route Planning in Transportation Networks" surveys the recent advances in algorithms designed to handle routing in various transportation networks. This includes road, public transit, and multimodal systems. The focus is on both the theoretical underpinnings and practical applications, aiming to provide queries' efficiency and robustness across different scenarios.

Key Concepts and Models

Road Networks

In road networks, routing algorithms have evolved to answer queries in milliseconds across large, continental-scale graphs. The techniques involve a balance between preprocessing effort, space requirements, and query time.

• Static Shortest Paths: Basic Dijkstra’s algorithm, bidirectional search, and A* algorithm are foundational. However, these methods have seen significant enhancements through goal-directed techniques, geometric containers, and hierarchical methods such as Contraction Hierarchies (CH) and Transit Node Routing (TNR).
• Dynamic Networks: Algorithms such as PHAST (for hardware-accelerated shortest path trees) improve preprocessing efficiency, allowing rapid updates in dynamic scenarios.
• Time-Dependent Shortest Paths: Techniques like time-dependent search and SHARC are applied to accommodate predictable variations in travel times, ensuring timely responses to queries considering current traffic conditions.

Public Transit Networks

Public transit routing is inherently more complex due to its time-dependent and multicriteria nature.

• Models: Both time-expanded models, which unroll the time-dependent timetable into a larger static graph, and time-dependent models, which directly handle time-varying travel costs, are used.
• Algorithms:
  • Earliest Arrival: Algorithms like Connection Scan Algorithm (CSA) operate on an acyclic space-time graph for efficiency.
  • Range Queries: These are handled by extended variants of Dijkstra’s algorithm that manage travel-time functions over a period.
  • Multicriteria Problems: RAPTOR is prominent for its efficiency in computing multiple criteria such as earliest arrival and number of transfers in rounds.

Multimodal Journey Planning

Involves combining different modes of transport such as walking, driving, and public transit in a single journey. The paper examines techniques like Access-Node Routing (ANR) and State-Dependent ALT (SDALT) that incorporate user-defined constraints and optimize diverse sets of routes based on criteria beyond travel time, like cost and convenience.

Performance Analysis

Simplified vs. Realistic Models

The findings indicate significant differences in algorithm performance between simplified and realistic road network models.

• Simplified Models disregard turn costs and restrictions, leading to generally faster query times. Techniques like CH and TNR perform well under these conditions.
• Realistic Models include turn penalties, thus requiring more sophisticated methods like Customizable Route Planning (CRP) to maintain efficiency. CRP excels by only requiring a fast metric-dependent customization phase to incorporate new metrics.

Public Transit Network Experiments

Algorithms are benchmarked for metropolitan and larger-scale public transit networks.

• Exact Algorithms: RAPTOR and CSA deliver efficient query performance without preprocessing, but preprocessing-based methods like Transfer Patterns offer superior speeds and scalability.
• Multicriteria Optimization: RAPTOR outperforms traditional methods, effectively handling additional criteria like fare zones and reliability.

Implications and Future Work

The research highlights several implications:

• Scalability and Flexibility: Real-world applications need scalable algorithms flexible enough to handle multiple metrics and dynamic changes (e.g., CRP and RAPTOR).
• Integration of Real-Time Data: Incorporating real-time traffic and schedule information remains challenging but essential for creating truly comprehensive routing solutions.
• Personalization: Future algorithms should consider user preferences more deeply, providing tailored routing solutions that go beyond one-size-fits-all approaches.

Overall, while significant strides have been made in both theoretical developments and practical deployments, the end goal of a worldwide, multimodal journey planner that incorporates real-time data and personalized preferences remains ahead. Given the rapid advancements in this field, continuous research and development are likely to bring this aspiration within reach.