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

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