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Gathering Asynchronous Robots in a Tree Sruti Gan Chaudhuri Jadavpur University, India GRASTA-MAC 2015 Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 1 / 27 Definition of the problem

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Gathering Asynchronous Robots in a Tree

Sruti Gan Chaudhuri

Jadavpur University, India

GRASTA-MAC 2015

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Definition of the problem

Given a tree

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Definition of the problem

Given a tree Randomly distributed mobile agents/robots (autonomous, homogeneous, non distinguishable, silent) in nodes

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Definition of the problem

Given a tree Randomly distributed mobile agents/robots (autonomous, homogeneous, non distinguishable, silent) in nodes The robots have to gather at a single node

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Computational model

Robots have no identity Nodes and edges of the graphs are not marked The robots have their local coordinate systems

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Computational model

LOOK

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Computational model

COMPUTE DESTINATION

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Computational model

MOVE

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Computational model

Oblivious: forget earlier computations. No multiplicity detection capabilities. Activation Schedule: Synchronous/Semi synchronous/Asynchronous

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Motivation

Results 1:

Gathering in graph in general is not possible even with synchronicity.

Ref: Gabriele Di Stefano, Alfredo Navarra, Optimal Gathering of Oblivious Robots in Anonymous Graphs, SIROCCO 2013, Volume 8179 of the series Lecture Notes in Computer Science pp 213-224.

Results 2

Gathering in plane in general is not possible.

(Ref: 1. Pierre Courtieu, Lionel Rieg, S´ ebastien Tixeuil, Xavier Urbain, Impossibility of gathering, a certification, Information Processing Letters, Volume 115, Issue 3, March 2015, Pages 447-45.

2. Paola Flocchini, Giuseppe Prencipe, Nicola Santoro, Distributed Computing by Oblivious Mobile Robots, Synthesis Lectures
n Distributed Computing Theory August 2012, Chapter 3, pages 17 - 61.)

Results 3

Gathering in plane is possible with agreement in coordinate axes even when the robots have limited visibility.

Ref: Paola Flocchini, Giuseppe Prencipe, Nicola Santoro, Peter Widmayer, Gathering of asynchronous robots with limited visibility, Theoretical Computer Science, Volume 337, Issues 1–3, 9 June 2005, Pages 147-168,

Results 4

Samuel Guilbault, Andrzej Pelc, Gathering asynchronous oblivious agents with local vision in regular bipartite graphs, Journal Theoretical Computer Science, Volume 509, October, 2013 Pages 86-96.

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Some open questions

Many results in gathering in grid, ring consider the knowledge of multiplicity detection. Can we remove this? All the results in continuous domain under Synchronous, Semi synchronous or Asynchronous model, do not hold in discrete domain. E.g., Gathering is possible under synchronous model in continuous domain but not in discrete domain. Whan happens in Limited visibility in general graph?

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Gathering in tree under limited visibility

No multiplicity detection Asynchronous Limited visibility

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When destination is given

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When destination is given

Eliminate the peripheral nodes The robots only remember their parents

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When destination is given

Eliminate the peripheral nodes The robots only remember their parents Use pebbles 1 to mark path towards leaf

1Balasingham Balamohan, Stefan Dobrev, Paola Flocchini, and Nicola Santoro. Asynchronous exploration of an unknown anonymous dangerous graph with o (1) pebbles. In SIROCCO, pages 279–290. Springer, 2012. Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 15 / 27

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Movement strategy for a robot

If I see a robot in neighbor(which is not destination) node, I will not move

Assured

The robots will not toggle The robots will not be in deadlock: there always be a robot which will move unless it is already in destination.

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When the destination is not given

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When the robots are completely oblivious

The graph (drawing) is oriented. Visibility graph of the robots is connected.

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When the robots are completely oblivious

The graph (drawing) is oriented. Visibility graph of the robots is connected. The robots gather to one of the corner most nodes, e.g., at down-right most node which has a robot.

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Movement strategy for a robot

If I see a robot in more than one neighboring nodes, I will not move.

No Move

Assured

The visibility graph will not be disconnected.

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Movement strategy for a robot

If I see a robot in more than one neighboring nodes, I will not move. Else If I see a robot below my horizontal axis , I move to that node.

Assured

The visibility graph will not be disconnected.

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Movement strategy for a robot

If I see a robot in more than one neighboring nodes, I will not move. Else If I see a robot below my horizontal axis , I move to that node. OR If I see a robot right to my vertical axis, I move to that node.

Assured

The visibility graph will not be disconnected. The robots will move to the right-down most roots.

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Gathering in tree under limited visibility

Gathering in Tree Under Limitted Visibility Gathering node given Gathering node not given The robots are not completely oblivious The robots are completely oblivious The graph is oriented

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Gathering in tree under limited visibility

Gathering in Tree Under Limitted Visibility Gathering node given Gathering node not given The robots are not completely oblivious The robots are completely oblivious The graph is oriented

True for Grids in many cases

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On going development

What happens if the Graph is not oriented? To explore the limited visibility model in general graph Optimizing the robots movement Collision avoidence algorithm Directed Graph (characterization) ...

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Acknowledgement

Krishnendu Mukhopadhyaya (Professor), ISI, Kolkata, India. Sumitro Bhawmik (Research Scholar), IIT Kharagpur, India. Srabani Mukhopadhyaya (Professor), BITM, Kolkata, India.

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Thank You

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