32 research outputs found
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
An algorithm with improved complexity for pebble motion/multi-agent path finding on trees
The pebble motion on trees (PMT) problem consists in finding a feasible
sequence of moves that repositions a set of pebbles to assigned target
vertices. This problem has been widely studied because, in many cases, the more
general Multi-Agent path finding (MAPF) problem on graphs can be reduced to
PMT.
We propose a simple and easy to implement procedure, which finds solutions of
length O(knc + n^2), where n is the number of nodes, is the number of
pebbles, and c the maximum length of corridors in the tree. This complexity
result is more detailed than the current best known result O(n^3), which is
equal to our result in the worst case, but does not capture the dependency on c
and k
A systematic literature review of multi-agent pathfinding for maze research
Multi-agent Pathfinding, also known as MAPF, is
an Artificial Intelligence problem-solving. The aim is to
direct each agent to find its path to reach its target, both
individually and in groups. Of course, this path allows agents
to move without colliding with each other. This MAPF
application is implemented in many areas that require the
movement of various agents, such as warehouse robots,
autonomous cars, video games, traffic control, Unmanned
Aerial Vehicles (UAV), Search and Rescue (SAR), many
others. The use of multi-agent in exploring often assumes all
areas to be explored are free of obstructions. However, the
use of MAPF to achieve their goals often faces static barriers,
and even other agents can also be considered dynamic
barriers. Because it requires some constraints in the program,
such as agents cannot collide with each other. The use of
single-agent can find the shortest path through exploration.
Still, multi-agent cooperation should shorten the time to find
a target location, especially if there is more than one target.
This paper explains the Systematic Literature Review (SLR)
method to review research on various multi-agent
pathfinding. The contribution of this paper is the analysis of
multi-agent pathfinding and its potential application in
solving maze problems based on an SLR
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