6,118 research outputs found
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
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
Landmark Guided Probabilistic Roadmap Queries
A landmark based heuristic is investigated for reducing query phase run-time
of the probabilistic roadmap (\PRM) motion planning method. The heuristic is
generated by storing minimum spanning trees from a small number of vertices
within the \PRM graph and using these trees to approximate the cost of a
shortest path between any two vertices of the graph. The intermediate step of
preprocessing the graph increases the time and memory requirements of the
classical motion planning technique in exchange for speeding up individual
queries making the method advantageous in multi-query applications. This paper
investigates these trade-offs on \PRM graphs constructed in randomized
environments as well as a practical manipulator simulation.We conclude that the
method is preferable to Dijkstra's algorithm or the algorithm with
conventional heuristics in multi-query applications.Comment: 7 Page
JGraphT -- A Java library for graph data structures and algorithms
Mathematical software and graph-theoretical algorithmic packages to
efficiently model, analyze and query graphs are crucial in an era where
large-scale spatial, societal and economic network data are abundantly
available. One such package is JGraphT, a programming library which contains
very efficient and generic graph data-structures along with a large collection
of state-of-the-art algorithms. The library is written in Java with stability,
interoperability and performance in mind. A distinctive feature of this library
is the ability to model vertices and edges as arbitrary objects, thereby
permitting natural representations of many common networks including
transportation, social and biological networks. Besides classic graph
algorithms such as shortest-paths and spanning-tree algorithms, the library
contains numerous advanced algorithms: graph and subgraph isomorphism; matching
and flow problems; approximation algorithms for NP-hard problems such as
independent set and TSP; and several more exotic algorithms such as Berge graph
detection. Due to its versatility and generic design, JGraphT is currently used
in large-scale commercial, non-commercial and academic research projects. In
this work we describe in detail the design and underlying structure of the
library, and discuss its most important features and algorithms. A
computational study is conducted to evaluate the performance of JGraphT versus
a number of similar libraries. Experiments on a large number of graphs over a
variety of popular algorithms show that JGraphT is highly competitive with
other established libraries such as NetworkX or the BGL.Comment: Major Revisio
Combining Subgoal Graphs with Reinforcement Learning to Build a Rational Pathfinder
In this paper, we present a hierarchical path planning framework called SG-RL
(subgoal graphs-reinforcement learning), to plan rational paths for agents
maneuvering in continuous and uncertain environments. By "rational", we mean
(1) efficient path planning to eliminate first-move lags; (2) collision-free
and smooth for agents with kinematic constraints satisfied. SG-RL works in a
two-level manner. At the first level, SG-RL uses a geometric path-planning
method, i.e., Simple Subgoal Graphs (SSG), to efficiently find optimal abstract
paths, also called subgoal sequences. At the second level, SG-RL uses an RL
method, i.e., Least-Squares Policy Iteration (LSPI), to learn near-optimal
motion-planning policies which can generate kinematically feasible and
collision-free trajectories between adjacent subgoals. The first advantage of
the proposed method is that SSG can solve the limitations of sparse reward and
local minima trap for RL agents; thus, LSPI can be used to generate paths in
complex environments. The second advantage is that, when the environment
changes slightly (i.e., unexpected obstacles appearing), SG-RL does not need to
reconstruct subgoal graphs and replan subgoal sequences using SSG, since LSPI
can deal with uncertainties by exploiting its generalization ability to handle
changes in environments. Simulation experiments in representative scenarios
demonstrate that, compared with existing methods, SG-RL can work well on
large-scale maps with relatively low action-switching frequencies and shorter
path lengths, and SG-RL can deal with small changes in environments. We further
demonstrate that the design of reward functions and the types of training
environments are important factors for learning feasible policies.Comment: 20 page
Geometric shortest path containers [online]
In this paper, we consider Dijkstra\u27s algorithm for the
single source single target shortest path problem in large
sparse graphs.
The goal is to reduce the response time for on-line queries by
using precomputed information.
Due to the size of the graph, preprocessing space requirements
can be only linear in the number of nodes.
We assume that a layout of the graph is given.
In the preprocessing, we determine from this layout a geometric
object for each edge containing all nodes that can be reached by
a shortest path starting with that edge.
Based on these geometric objects, the search space for on-line
computation can be reduced significantly.
Shortest path queries can then be answered by Dijkstra\u27s
algorithm restricted to edges where the corresponding geometric
object contains the target.
We present an extensive experimental study comparing the impact
of different types of objects.
The test data we use are real-world traffic networks, the
typical field of application for this scenario.
Furthermore, we present new algorithms as well as an empirical
study for the dynamic case of this problem, where edge weights
are subject to change and the geometric containers have to be
updated.
We evaluate the quality and the time for different update
strategies that guarantee correct shortest paths.
Finally, we present a software framework in C++ to realize the
implementations of all of our variants of Dijkstra\u27s algorithm.
A basic implementation of the algorithm is refined for each
modification and - even more importantly - these modifications
can be combined in any possible way without loss of efficiency
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