69,122 research outputs found
Obstacle Numbers of Planar Graphs
Given finitely many connected polygonal obstacles in the
plane and a set of points in general position and not in any obstacle, the
{\em visibility graph} of with obstacles is the (geometric)
graph with vertex set , where two vertices are adjacent if the straight line
segment joining them intersects no obstacle. The obstacle number of a graph
is the smallest integer such that is the visibility graph of a set of
points with obstacles. If is planar, we define the planar obstacle
number of by further requiring that the visibility graph has no crossing
edges (hence that it is a planar geometric drawing of ). In this paper, we
prove that the maximum planar obstacle number of a planar graph of order is
, the maximum being attained (in particular) by maximal bipartite planar
graphs. This displays a significant difference with the standard obstacle
number, as we prove that the obstacle number of every bipartite planar graph
(and more generally in the class PURE-2-DIR of intersection graphs of straight
line segments in two directions) of order at least is .Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
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
Graphs with Plane Outside-Obstacle Representations
An \emph{obstacle representation} of a graph consists of a set of polygonal
obstacles and a distinct point for each vertex such that two points see each
other if and only if the corresponding vertices are adjacent. Obstacle
representations are a recent generalization of classical polygon--vertex
visibility graphs, for which the characterization and recognition problems are
long-standing open questions.
In this paper, we study \emph{plane outside-obstacle representations}, where
all obstacles lie in the unbounded face of the representation and no two
visibility segments cross. We give a combinatorial characterization of the
biconnected graphs that admit such a representation. Based on this
characterization, we present a simple linear-time recognition algorithm for
these graphs. As a side result, we show that the plane vertex--polygon
visibility graphs are exactly the maximal outerplanar graphs and that every
chordal outerplanar graph has an outside-obstacle representation.Comment: 12 pages, 7 figure
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
Accelerating Reinforcement Learning by Composing Solutions of Automatically Identified Subtasks
This paper discusses a system that accelerates reinforcement learning by
using transfer from related tasks. Without such transfer, even if two tasks are
very similar at some abstract level, an extensive re-learning effort is
required. The system achieves much of its power by transferring parts of
previously learned solutions rather than a single complete solution. The system
exploits strong features in the multi-dimensional function produced by
reinforcement learning in solving a particular task. These features are stable
and easy to recognize early in the learning process. They generate a
partitioning of the state space and thus the function. The partition is
represented as a graph. This is used to index and compose functions stored in a
case base to form a close approximation to the solution of the new task.
Experiments demonstrate that function composition often produces more than an
order of magnitude increase in learning rate compared to a basic reinforcement
learning algorithm
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