Hierarchical Time-Dependent Oracles

  title={Hierarchical Time-Dependent Oracles},
  author={Spyros C. Kontogiannis and Dorothea Wagner and Christos D. Zaroliagis},
We study networks obeying time-dependent min-cost path metrics, and present novel oracles for them which provably achieve two unique features: (i) subquadratic preprocessing time and space, independent of the metric’s amount of disconcavity; (ii) sublinear query time, in either the network size or the actual Dijkstra-Rank of the query at hand. 

Figures and Tables from this paper

An Axiomatic Approach to Time-Dependent Shortest Path Oracles

This work presents an axiomatic approach which shows that for directed networks that satisfy certain properties the authors can provide time-dependent distance oracles that provably exhibit subquadratic preprocessing time and space (independent of the metric’s amount of disconcavity).

Time-Dependent Alternative Route Planning: Theory and Practice

A novel query algorithm, called Time-Dependent Alternative Graph (TDAG), that exploits the outcome of a time-consuming preprocessing phase to create a manageable amount of travel-time metadata, in order to provide answers for arbitrary alternative-routes queries, in only a few milliseconds for continental-size instances.

Time-Dependent Alternative Route Planning

This work presents a new method for computing a set of alternative origin-to-destination routes in road networks with an underlying time-dependent metric that is characterized by minimum route overlap, small stretch factor, small size and low complexity.

A Cloud-Based Time-Dependent Routing Service

This work describes the architecture of the time-dependent routing engine, consisting of a core routing module along with the so-called urban-traffic knowledge base, which creates, maintains and stores historic traffic data, as well as live traffic updates such as road blockages or unforeseen congestion.

Algorithms for Cloud-Based Smart Mobility

This work reviews some recent innovative algorithmic approaches that contributed decisively in the development of efficient and effective cloud-based systems for smart mobility in urban environments.



Engineering Oracles for Time-Dependent Road Networks

This work significantly improves the FLAT oracle, improving the previous query time by $30\% and doubling the Dijkstra-rank speedup, and implements and experimentally evaluates a novel oracle (HORN), based on a landmark hierarchy, achieving even better performance wrt to FLAT.

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

Analysis and Experimental Evaluation of Time-Dependent Distance Oracles

This work presents oracles for providing time-dependent min-cost route plans, and proposes three query algorithms to efficiently provide min- cost route plan responses to arbitrary queries, and conducts an extensive, comparative experimental study with all query algorithms and six landmark sets.

Distance Oracles for Stretch Less Than 2

For the realistic case of sparse graphs, the distance oracles presented exhibit a smooth three-way trade-off between space, stretch and query time --- a phenomenon that does not occur in dense graphs.

Approximate distance oracles with improved preprocessing time

This work shows that for some universal constant c, a (2k − 1)-approximate distance oracle for G of size O(kn1+1/k) can be constructed in [EQUATION] time and can answer queries in O(k) time and gives an oracle which is faster for smaller k.

Distance Oracles for Sparse Graphs

A new lower bound for approximate distance oracles in the cell-probe model is given, which holds even for sparse (polylog(n)-degree) graphs, and it is not an "incompressibility" bound: it is a three-way tradeoff between space, stretch, and query time.

Preprocess, Set, Query!

It is shown that it is possible to break the stretch 2 barrier at the price of non-constant query time in unweighted undirected graphs.

On the Complexity of Time-Dependent Shortest Paths

This work investigates the complexity of shortest paths in time-dependent graphs where the costs of edges vary as a function of time, and shows that when the edge cost functions are (polynomial-size) piecewise linear, the shortest path from s to d can change nΘ(logn) times.

Shortest-path queries in static networks

This survey reviews selected approaches, algorithms, and results on shortest-path queries from these fields, with the main focus lying on the tradeoff between the index size and the query time.

Compact oracles for reachability and approximate distances in planar digraphs

  • M. Thorup
  • Computer Science, Mathematics
  • 2004
The technique is based on a novel dipath decomposition of planar digraphs that instead of using the standard separator with O(/spl radic/n) vertices, in effect finds a separator using a constant number of dipaths.