Improved Dispersion of Mobile Robots on Arbitrary Graphs

12/13/2018
by   Anisur Rahaman Molla, et al.
0

The dispersion problem on graphs asks k≤ n robots placed initially arbitrarily on the nodes of an n-node graph to reposition autonomously to reach a configuration in which each robot is at a distinct node of the graph. This problem is of significant interest due to its relationship to other fundamental robot coordination problems, such as exploration, scattering, load balancing, etc. The goal is to develop both memory- and time-efficient algorithms. We provide an algorithm solving dispersion in O({m,Δ k}) time using O( ({Δ, k}))-bits at each robot in the robot-only memory model -- the robots have memory but not the nodes of the graph, where m is the number of edges and Δ is the maximum degree of any node in the graph. The runtime is optimal for bounded-degree graphs (Δ=O(1)) and improves significantly the O(mn) time of the best previously known algorithm. We provide two algorithms solving dispersion in the whiteboard model -- each node of the graph also has memory in addition to the memory at each robot. The first algorithm has O(m) time with O(Δ)-bits at each node and O( k)-bits at each robot. The second algorithm has O({m,Δ k}) time with O( ({Δ,k}))-bits at each node and O( k)-bits at each robot. These are the first terminating algorithms for dispersion. The second algorithm is time-optimal for bounded-degree graphs. We provide an algorithm solving dispersion in O(k) time in the whiteboard model enhanced with local messaging -- a robot visiting a node can send messages to the neighbors of that node, with O(Δ)-bits at each node and O( k)-bits at each robot. This is the first time-optimal algorithm for arbitrary graphs with termination guarantees.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
09/04/2019

Dispersion of Mobile Robots in the Global Communication Model

The dispersion problem on graphs asks k≤ n robots placed initially arbit...
research
05/30/2018

Efficient Dispersion of Mobile Robots on Graphs

The dispersion problem on graphs requires k robots placed arbitrarily at...
research
06/07/2021

Near-Optimal Dispersion on Arbitrary Anonymous Graphs

Given an undirected, anonymous, port-labeled graph of n memory-less node...
research
08/03/2020

Memory Optimal Dispersion by Anonymous Mobile Robots

Consider a team of k ≤ n autonomous mobile robots initially placed at a ...
research
07/20/2020

Push, Stop, and Replan: An Application of Pebble Motion on Graphs to Planning in Automated Warehouses

The pebble-motion on graphs is a subcategory of multi-agent pathfinding ...
research
02/27/2019

Dispersion of Mobile Robots: The Power of Randomness

We consider cooperation among insects, modeled as cooperation between mo...
research
04/23/2020

Efficient Dispersion on an Anonymous Ring in the Presence of Byzantine Robots

The problem of dispersion of mobile robots on a graph asks that n robots...

Please sign up or login with your details

Forgot password? Click here to reset