1,152 research outputs found
Feasibility of Motion Planning on Acyclic and Strongly Connected Directed Graphs
Motion planning is a fundamental problem of robotics with applications in
many areas of computer science and beyond. Its restriction to graphs has been
investigated in the literature for it allows to concentrate on the
combinatorial problem abstracting from geometric considerations. In this paper,
we consider motion planning over directed graphs, which are of interest for
asymmetric communication networks. Directed graphs generalize undirected
graphs, while introducing a new source of complexity to the motion planning
problem: moves are not reversible. We first consider the class of acyclic
directed graphs and show that the feasibility can be solved in time linear in
the product of the number of vertices and the number of arcs. We then turn to
strongly connected directed graphs. We first prove a structural theorem for
decomposing strongly connected directed graphs into strongly biconnected
components.Based on the structural decomposition, we give an algorithm for the
feasibility of motion planning on strongly connected directed graphs, and show
that it can also be decided in time linear in the product of the number of
vertices and the number of arcs.Comment: 19 pages, 9 figures, algorithm2e.st
On the Computational Complexity of Multi-Agent Pathfinding on Directed Graphs
The determination of the computational complexity of multi-agent pathfinding
on directed graphs has been an open problem for many years. For undirected
graphs, solvability can be decided in polynomial time, as has been shown
already in the eighties. Further, recently it has been shown that a special
case on directed graphs is solvable in polynomial time. In this paper, we show
that the problem is NP-hard in the general case. In addition, some upper bounds
are proven
Reconfiguring Directed Trees in a Digraph
In this paper, we investigate the computational complexity of subgraph
reconfiguration problems in directed graphs. More specifically, we focus on the
problem of determining whether, given two directed trees in a digraph, there is
a (reconfiguration) sequence of directed trees such that for every pair of two
consecutive trees in the sequence, one of them is obtained from the other by
removing an arc and then adding another arc. We show that this problem can be
solved in polynomial time, whereas the problem is PSPACE-complete when we
restrict directed trees in a reconfiguration sequence to form directed paths.
We also show that there is a polynomial-time algorithm for finding a shortest
reconfiguration sequence between two directed spanning trees.Comment: 10 page
On the Minimal Revision Problem of Specification Automata
As robots are being integrated into our daily lives, it becomes necessary to
provide guarantees on the safe and provably correct operation. Such guarantees
can be provided using automata theoretic task and mission planning where the
requirements are expressed as temporal logic specifications. However, in
real-life scenarios, it is to be expected that not all user task requirements
can be realized by the robot. In such cases, the robot must provide feedback to
the user on why it cannot accomplish a given task. Moreover, the robot should
indicate what tasks it can accomplish which are as "close" as possible to the
initial user intent. This paper establishes that the latter problem, which is
referred to as the minimal specification revision problem, is NP complete. A
heuristic algorithm is presented that can compute good approximations to the
Minimal Revision Problem (MRP) in polynomial time. The experimental study of
the algorithm demonstrates that in most problem instances the heuristic
algorithm actually returns the optimal solution. Finally, some cases where the
algorithm does not return the optimal solution are presented.Comment: 23 pages, 16 figures, 2 tables, International Joural of Robotics
Research 2014 Major Revision (submitted
Survey on assembly sequencing: a combinatorial and geometrical perspective
A systematic overview on the subject of assembly sequencing is presented. Sequencing lies at the core of assembly planning, and variants include finding a feasible sequence—respecting the precedence constraints between the assembly operations—, or determining an optimal one according to one or several operational criteria. The different ways of representing the space of feasible assembly sequences are described, as well as the search and optimization algorithms that can be used. Geometry plays a fundamental role in devising the precedence constraints between assembly operations, and this is the subject of the second part of the survey, which treats also motion in contact in the context of the actual performance of assembly operations.Peer ReviewedPostprint (author’s final draft
Minimum -vertex strongly biconnected spanning directed subgraph problem
A directed graph is strongly biconnected if is strongly
connected and its underlying graph is biconnected. A strongly biconnected
directed graph is called -vertex-strongly biconnected if and the induced subgraph on is
strongly biconnected for every vertex . In this paper we study the
following problem.
Given a -vertex-strongly biconnected directed graph , compute an
edge subset of minimum size such that the subgraph
is -vertex-strongly biconnected
Minimum -edge strongly biconnected spanning directed subgraph problem
Wu and Grumbach introduced the concept of strongly biconnected directed
graphs. A directed graph is called strongly biconnected if the
directed graph is strongly connected and the underlying undirected graph of
is biconnected. A strongly biconnected directed graph is said to
be - edge strongly biconnected if it has at least three vertices and the
directed subgraph is strongly
biconnected for all . Let be a -edge-strongly biconnected
directed graph. In this paper we study the problem of computing a minimum size
subset such that the directed subgraph is - edge
strongly biconnected
- …