Customizable Contraction Hierarchies

@article{Dibbelt2016CustomizableCH,
  title={Customizable Contraction Hierarchies},
  author={Julian Dibbelt and Ben Strasser and Dorothea Wagner},
  journal={Journal of Experimental Algorithmics (JEA)},
  year={2016},
  volume={21},
  pages={1 - 49}
}
We consider the problem of quickly computing shortest paths in weighted graphs. Often, this is achieved in two phases: (1) derive auxiliary data in an expensive preprocessing phase, and (2) use this auxiliary data to speed up the query phase. By adding a fast weight-customization phase, we extend Contraction Hierarchies to support a three-phase workflow. The expensive preprocessing is split into a phase exploiting solely the unweighted topology of the graph and a lightweight phase that adapts… 
Faster and Better Nested Dissection Orders for Customizable Contraction Hierarchies
TLDR
This work considers the acceleration of shortest path queries in road networks using Customizable Contraction Hierarchies (CCH), based on computing a nested dissection order by recursively dividing the road network into parts by using FlowCutter and Inertial Flow.
Accelerating Traffic Assignment with Customizable Contraction Hierarchies
TLDR
The recently developed customizable contraction hierarchies are used for both shortest path search and network loading in the bi-conjugate Frank–Wolfe algorithm and achieve a speedup by a factor of 42 compared with a straightforward implementation of Dijkstra’s algorithm.
Contracting and Compressing Shortest Path Databases
TLDR
In a range of experiments on road networks, it is shown that CH-CPD substantially improves on conventional CPDs in terms of preprocessing costs and online performance, and a new bi-directional path extraction algorithm which is described which is called CHCPD.
GPU road network graph contraction and SSSP query
TLDR
A GPU contraction algorithm, CU-CH, is presented which overcomes issues such as the validity of simultaneous potentially overlapping searches, score staleness, and parallel graph updates by partitioning the graph into levels composed of independent sets of nodes (non-adjacent nodes) with similar scores.
Engineering Data Reduction for Nested Dissection
TLDR
This paper engineer new data reduction rules for the minimum fill-in problem, which significantly reduce the size of the graph while producing an equivalent (or near-equivalent) instance by applying both new and existing data reduction Rules exhaustively before nested dissection.
Fast GPU Graph Contraction by Combining Efficient Shallow Searches and Post-Culling
TLDR
Efficient GPU single-source shortest-path queries of road network graphs can be realized by a technique called PHAST in which the graph is contracted once and the resulting contracted graph is queried as needed, resulting in efficient queries.
Customizable Contraction Hierarchies with Turn Costs
TLDR
This work carefully engineer CCH to exploit different properties of the expanded graph, and reduces the increase in customization time from up to an order of magnitude to a factor of about 3.5, and presents a CCH variant that works on the compact model, and shows that it performs worse than the variant on the edge-based model.
Provable Efficiency of Contraction Hierarchies with Randomized Preprocessing
TLDR
This work introduces a method to construct randomized Contraction Hierarchies on road networks as well as a probabilistic query routine and reveals that randomized CH lead to sublinear search space sizes, auxiliary data, and correct query results with high probability after a polynomial time preprocessing phase.
Intriguingly Simple and Efficient Time-Dependent Routing in Road Networks
TLDR
A highlight of the introduced algorithms is that they do not rely on linking and merging profile functions and are small enough to be able to efficiently implement profile queries using a simple sampling-based approach.
On k-Path Covers and their Applications
TLDR
Efficient algorithms that produce very small k-Path Covers for large real-world road networks (with a posteriori guarantees via instance-based lower bounds) are provided.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 84 REFERENCES
Graph Partitioning with Natural Cuts
TLDR
A novel approach to graph partitioning based on the notion of natural cuts, called PUNCH, which obtains the best known partitions for continental-sized networks, significantly improving on previous results.
Shortest Paths in Digraphs of Small Treewidth. Part I: Sequential Algorithms
Abstract. We consider the problem of preprocessing an n -vertex digraph with real edge weights so that subsequent queries for the shortest path or distance between any two vertices can be efficiently
Contraction Hierarchies: Faster and Simpler Hierarchical Routing in Road Networks
TLDR
CHs can be combined with many other route planning techniques, leading to improved performance for many-to-many routing, transit-node routing, goal-directed routing or mobile and dynamic scenarios, and a hierarchical query algorithm using bidirectional shortest-path search is obtained.
Faster Batched Shortest Paths in Road Networks
TLDR
It is concluded that a new extension of PHAST (a recent one-to-all algorithm), called RPHAST, has the best performance in most cases, often by orders of magnitude.
Faster Customization of Road Networks
TLDR
This work reduces customization time even further, by an order of magnitude, which makes it worthwhile even when a single query is to be run, enabling a host of new applications.
The Shortcut Problem - Complexity and Algorithms
TLDR
The algorithmic complexity of the shortcut problem is studied and approximation algorithms for a special graph class are given and how to stochastically evaluate a given shortcut assignment on graphs that are too large to do so exactly is shown.
Computing All-Pairs Shortest Paths by Leveraging Low Treewidth
TLDR
Two new, efficient algorithms for computing all-pairs shortest paths (APSP) make use of directed path consistency (DPC) along a vertex ordering d, which can be used for temporal and spatial reasoning, e.g. for the Simple Temporal Problem (STP).
Contraction Hierarchies on Grid Graphs
TLDR
This paper shows that contraction hierarchies can be applied to grid graphs as well, and points out interesting connections to speed-up techniques shaped for routing on grids, like swamp hierarchies and jump points, and provides experimental results for game maps, mazes, random grids and rooms.
Customizable Route Planning
We present an algorithm to compute shortest paths on continental road networks with arbitrary metrics (cost functions). The approach supports turn costs, enables real-time queries, and can
PHAST: Hardware-Accelerated Shortest Path Trees
TLDR
A novel algorithm to solve the nonnegative single-source shortest path problem on road networks and other graphs with low highway dimension that needs fewer operations, has better locality, and is better able to exploit parallelism at multi-core and instruction levels.
...
1
2
3
4
5
...