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Theory of Distributed Systems
Universal Shape Formation
for Programmable Matter(Thim Strothmann)
Joint work with
BDA 2016 – July 25, 2016
2
Theory of Distributed
Systems
Inspiration
BDA 2016
Video on this slide was deleted to decrease file size.
For inspiration Video (scene from Big Hero six) visit
https://www.youtube.com/watch?v=fF1rDKEC0TI.
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Theory of Distributed
Systems
Motivation - Applications
BDA 2016
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Theory of Distributed
Systems
The amoebot Model
BDA 2016
Overarching Constraint: Maintain Connectivity
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Theory of Distributed
Systems
The amoebot Model
BDA 2016
• “Standard” asynchronous computation model
• Only one particle is activated in each time step
• Once activated a particle can compute, communicate and perform one
move
• an adversary activates particles
• Round: every particle is activated at least once
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Theory of Distributed
Systems
Shape Formation Problem
BDA 2016
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Theory of Distributed
Systems
Naive Shape Formation Problem
BDA 2016
Video on this slide was deleted to decrease file size.
For naïve Shape Formation algorithms (Hexagon & Triangle) visit
http://sops.cs.upb.de/ .
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Theory of Distributed
Systems
Universal Shape Formation Problem
In general not possible, i.e.,
BDA 2016
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Theory of Distributed
Systems
Universal Shape Formation Problem
Input: constant size set of faces
Goal:
build shape given by faces (scaled-up and possibly rotated)
scale to include all particles
(no leftover particles)
BDA 2016
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Theory of Distributed
Systems
Universal Shape Formation Problem
BDA 2016
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Theory of Distributed
Systems
Universal Shape Formation Problem
Our Result:
Given any shape described by a constant number of faces, our algorithm
builds that shape using all particles in the system in 𝑂 𝑛 rounds.
BDA 2016
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Theory of Distributed
Systems
Universal Shape Formation Problem
Note: 𝑂 𝑛 rounds is not possible if we start in an arbitrary initial
configuration.
Solution:
BDA 2016
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Theory of Distributed
Systems
Universal Shape Formation Algorithm
Movement Primitives:
2) Triangle expansion/ contraction/ rotation (𝑂 ℓ rounds)
expansion contraction
rotation
ℓ
BDA 2016
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Theory of Distributed
Systems
Universal Shape Formation Algorithm
Intermediate Structure
BDA 2016
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Theory of Distributed
Systems
Universal Shape Formation Algorithm
Intermediate Structure
BDA 2016
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Theory of Distributed
Systems
Universal Shape Formation Algorithm
Building the final shape:
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7 9
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Theory of Distributed
Systems
Universal Shape Formation Algorithm
The devil is in the details:
Take care of the imperfection of the intermediate structure without
moving it.
Make up for the estimation errors of ℓ.
BDA 2016
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Theory of Distributed
Systems
Universal Shape Formation Algorithm
The devil is in the details:
Triangles have to be cut to different sizes (+ incorporate waste).
The intermediate structure might block the final building process
BDA 2016
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Theory of Distributed
Systems
Summary & Future Work
Result: Given any shape described by a constant number of faces, our
algorithm builds that shape using all particles in the system in 𝑂 𝑛rounds.
Interesting Challenges:
arbitrary configuration of low diameter
non-constant size shapes
3D
Failures
BDA 2016
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Theory of Distributed
Systems
References
Corresponding Publication:Zahra Derakhshandeh, Robert Gmyr, Andréa W. Richa, Christian Scheideler, Thim Strothmann:
Universal Shape Formation for Programmable Matter. SPAA 2016: 289-299
(http://doi.acm.org/10.1145/2935764.2935784)
For videos of some of our algorithms and a (slightly outdated)
publication history in the topic visit:http://sops.cs.upb.de/
BDA 2016
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