Cyclic network automata and cohomological waves

Yiqing Cai, Robert Ghrist

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

1 Scopus citations

Abstract

Following Baryshnikov-Coffman-Kwak [2], we use cyclic network automata (CNA) to generate a decentralized protocol for dynamic coverage problems in a sensor network, with only a small fraction of sensors awake at every moment. This paper gives a rigorous analysis of CNA and shows that waves of awake-state nodes automatically solve pusuit/evasion-type problems without centralized coordination. As a corollary of this work, we unearth some interesting topological interpretations of features previously observed in cyclic cellular automata (CCA). By considering CCA over networks and completing to simplicial complexes, we induce dynamics on the higher-dimensional complex. In this setting, waves are seen to be generated by topological defects with a nontrivial degree (or winding number). The simplicial complex has the topological type of the underlying map of the workspace (a subset of the plane), and the resulting waves can be classified cohomologically. This allows one to 'program' pulses in the sensor network according to cohomology class. We give a realization theorem for such pulse waves.

Original languageEnglish (US)
Title of host publicationIPSN 2014 - Proceedings of the 13th International Symposium on Information Processing in Sensor Networks (Part of CPS Week)
PublisherIEEE Computer Society
Pages215-224
Number of pages10
ISBN (Print)9781479931460
DOIs
StatePublished - 2014
Event13th IEEE/ACM International Conference on Information Processing in Sensor Networks, IPSN 2014 - Berlin, Germany
Duration: Apr 15 2014Apr 17 2014

Publication series

NameIPSN 2014 - Proceedings of the 13th International Symposium on Information Processing in Sensor Networks (Part of CPS Week)

Other

Other13th IEEE/ACM International Conference on Information Processing in Sensor Networks, IPSN 2014
CountryGermany
CityBerlin
Period4/15/144/17/14

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