Deterministic Leader Election in Programmable Matter

Addressing a fundamental problem in programmable matter, we present the first deterministic algorithm to elect a unique leader in a system of connected amoebots assuming only that amoebots are initially contracted. Previous algorithms either used randomization, made various assumptions (shapes with no holes, or known shared chirality), or elected several co-leaders in some cases. Some of the building blocks we introduce in constructing the algorithm are of interest by themselves, especially the procedure we present for reaching common chirality among the amoebots. Given the leader election and the chirality agreement building block, it is known that various tasks in programmable matter can be performed or improved. The main idea of the new algorithm is the usage of the ability of the amoebots to move, which previous leader election algorithms have not used.

[1]  Christian Scheideler,et al.  Universal coating for programmable matter , 2016, Theor. Comput. Sci..

[2]  Christian Scheideler,et al.  Leader Election and Shape Formation with Self-organizing Programmable Matter , 2015, DNA.

[3]  Christian Scheideler,et al.  Infinite Object Coating in the Amoebot Model , 2014, ArXiv.

[4]  Nicola Santoro,et al.  Line Recovery by Programmable Particles , 2018, ICDCN.

[5]  Christian Scheideler,et al.  Improved Leader Election for Self-organizing Programmable Matter , 2017, ALGOSENSORS.

[6]  Christian Scheideler,et al.  Universal Shape Formation for Programmable Matter , 2016, SPAA.

[7]  Dana Randall,et al.  A Markov Chain Algorithm for Compression in Self-Organizing Particle Systems , 2016, PODC.

[8]  Tommaso Toffoli,et al.  Programmable Matter: Concepts and Realization , 1993, Int. J. High Speed Comput..

[9]  Adrian Segall,et al.  Distributed network protocols , 1983, IEEE Trans. Inf. Theory.

[10]  Rida A. Bazzi,et al.  Brief Announcement: Deterministic Leader Election in Self-organizing Particle Systems , 2018, SSS.

[11]  Christian Scheideler,et al.  Amoebot - a new model for programmable matter , 2014, SPAA.

[12]  Dana Randall,et al.  A Stochastic Approach to Shortcut Bridging in Programmable Matter , 2017, DNA.

[13]  Olivier Togni,et al.  Distributed leader election and computation of local identifiers for programmable matter , 2018, ALGOSENSORS.

[14]  Yukiko Yamauchi,et al.  Shape formation by programmable particles , 2019, Distributed Computing.

[15]  Christian Scheideler,et al.  An Algorithmic Framework for Shape Formation Problems in Self-Organizing Particle Systems , 2015, NANOCOM.

[16]  Christian Scheideler,et al.  On the runtime of universal coating for programmable matter , 2016, Natural Computing.

[17]  Christian Scheideler,et al.  Computing by Programmable Particles , 2019, Distributed Computing by Mobile Entities.

[18]  Christian Scheideler,et al.  Convex Hull Formation for Programmable Matter , 2018, ICDCN.