Convex Hull Formation for Programmable Matter

Joshua J. Daymude, Robert Gmyr, Kristian Hinnenthal, Irina Kostitsyna, Christian Scheideler, Andréa W. Richa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations


We envision programmable matter as a system of nanoscale agents (called particles) with very limited computational capabilities that move and compute collectively to achieve a desired goal. Motivated by the problem of sealing an object using minimal resources, we show how a particle system can self-organize to form an object's convex hull. We give a distributed, local algorithm for convex hull formation and prove that it runs in O(B) asynchronous rounds, where B is the length of the object's boundary. Within the same asymptotic runtime, this algorithm can be extended to also form the object's (weak) O-hull, which uses the same number of particles but minimizes the area enclosed by the hull. Our algorithms are the first to compute convex hulls with distributed entities that have strictly local sensing, constant-size memory, and no shared sense of orientation or coordinates. Ours is also the first distributed approach to computing restricted-orientation convex hulls. This approach involves coordinating particles as distributed memory; thus, as a supporting but independent result, we present and analyze an algorithm for organizing particles with constant-size memory as distributed binary counters that efficiently support increments, decrements, and zero-tests - - even as the particles move.

Original languageEnglish (US)
Title of host publicationACM International Conference Proceeding Series
PublisherAssociation for Computing Machinery
ISBN (Print)9781450377515
StatePublished - 2020
Event21st International Conference on Distributed Computing and Networking, ICDCN 2020 - Kolkata, India
Duration: Jan 4 2020Jan 7 2020

Publication series

NameACM International Conference Proceeding Series
VolumePart F165625


Conference21st International Conference on Distributed Computing and Networking, ICDCN 2020


  • computational geometry
  • convex hull
  • distributed algorithms
  • programmable matter
  • restricted-orientation geometry
  • self-organization

ASJC Scopus subject areas

  • Software
  • Human-Computer Interaction
  • Computer Vision and Pattern Recognition
  • Computer Networks and Communications


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