Distance Oracles for Time-Dependent Networks

We present the first approximate distance oracle for sparse directed networks with time-dependent arc-travel-times determined by continuous, piecewise linear, positive functions possessing the FIFO property. Our approach precomputes $(1+\epsilon)-$approximate distance summaries from selected landmark vertices to all other vertices in the network. Our oracle uses subquadratic space and time preprocessing, and provides two sublinear-time query algorithms that deliver constant and $(1+\sigma)-$approximate shortest-travel-times, respectively, for arbitrary origin-destination pairs in the network, for any constant $\sigma > \epsilon$. Our oracle is based only on the sparsity of the network, along with two quite natural assumptions about travel-time functions which allow the smooth transition towards asymmetric and time-dependent distance metrics.Comment: A preliminary version appeared as Technical Report ECOMPASS-TR-025 of EU funded research project eCOMPASS (http://www.ecompass-project.eu/). An extended abstract also appeared in the 41st International Colloquium on Automata, Languages, and Programming (ICALP 2014, track-A

Hierarchical Time-Dependent Oracles

We study networks obeying \emph{time-dependent} min-cost path metrics, and present novel oracles for them which \emph{provably} achieve two unique features: % (i) \emph{subquadratic} preprocessing time and space, \emph{independent} of the metric's amount of disconcavity; % (ii) \emph{sublinear} query time, in either the network size or the actual Dijkstra-Rank of the query at hand

Dynamic Time-Dependent Route Planning in Road Networks with User Preferences

There has been tremendous progress in algorithmic methods for computing driving directions on road networks. Most of that work focuses on time-independent route planning, where it is assumed that the cost on each arc is constant per query. In practice, the current traffic situation significantly influences the travel time on large parts of the road network, and it changes over the day. One can distinguish between traffic congestion that can be predicted using historical traffic data, and congestion due to unpredictable events, e.g., accidents. In this work, we study the \emph{dynamic and time-dependent} route planning problem, which takes both prediction (based on historical data) and live traffic into account. To this end, we propose a practical algorithm that, while robust to user preferences, is able to integrate global changes of the time-dependent metric~(e.g., due to traffic updates or user restrictions) faster than previous approaches, while allowing subsequent queries that enable interactive applications

Route Planning in Transportation Networks

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.Comment: This is an updated version of the technical report MSR-TR-2014-4, previously published by Microsoft Research. This work was mostly done while the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at Microsoft Research Silicon Valle

Improved Oracles for Time-Dependent Road Networks

A novel landmark-based oracle (CFLAT) is presented, which provides earliest-arrival-time route plans in time-dependent road networks. To our knowledge, this is the first oracle that preprocesses combinatorial structures (collections of time-stamped min-travel-time-path trees) rather than travel-time functions. The preprocessed data structure is exploited by a new query algorithm (CFCA) which also computes (and pays for it) the actual connecting path that preserves the theoretical approximation guarantees. To make it practical and tackle the main burden of landmark-based oracles (the large preprocessing requirements), CFLAT is extensively engineered. A thorough experimental evaluation on two real-world benchmark instances shows that CFLAT achieves a significant improvement on preprocessing, approximation guarantees and query-times, in comparison to previous landmark-based oracles. It also achieves competitive query-time performance compared to state-of-art speedup heuristics for time-dependent road networks, whose query-times in most cases do not account for path construction

Intelligent Traffic Management: From Practical Stochastic Path Planning to Reinforcement Learning Based City-Wide Traffic Optimization

This research focuses on intelligent traffic management including stochastic path planning and city scale traffic optimization. Stochastic path planning focuses on finding paths when edge weights are not fixed and change depending on the time of day/week. Then we focus on minimizing the running time of the overall procedure at query time utilizing precomputation and approximation. The city graph is partitioned into smaller groups of nodes and represented by its exemplar. In query time, source and destination pairs are connected to their respective exemplars and the path between those exemplars is found. After this, we move toward minimizing the city wide traffic congestion by making structural changes include changing the number of lanes, using ramp metering, varying speed limit, and modifying signal timing is possible. We propose a multi agent reinforcement learning (RL) framework for improving traffic flow in city networks. Our framework utilizes two level learning: a) each single agent learns the initial policy and b) multiple agents (changing the environment at the same time) update their policy based on the interaction with the dynamic environment and in agreement with other agents. The goal of RL agents is to interact with the environment to learn the optimal modification for each road segment through maximizing the cumulative reward over the set of possible actions in state space

Transit Node Routing Reconsidered

Transit Node Routing (TNR) is a fast and exact distance oracle for road networks. We show several new results for TNR. First, we give a surprisingly simple implementation fully based on Contraction Hierarchies that speeds up preprocessing by an order of magnitude approaching the time for just finding a CH (which alone has two orders of magnitude larger query time). We also develop a very effective purely graph theoretical locality filter without any compromise in query times. Finally, we show that a specialization to the online many-to-one (or one-to-many) shortest path further speeds up query time by an order of magnitude. This variant even has better query time than the fastest known previous methods which need much more space.Comment: 19 pages, submitted to SEA'201