Brief announcement: on reversible and irreversible conversions

Authors:
Mitre C. Dourado;Lucia Draque Penso;Dieter Rautenbach;Jayme L. Szwarcfiter
Affiliations:
Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brazil;Universität Ulm, Ulm, Germany;Universität Ulm, Ulm, Germany;Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brazil
Venue:
DISC'10 Proceedings of the 24th international conference on Distributed computing
Year:
2010

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Abstract

We study two types of iterative 0/1-vertex-labeling processes in arbitrary network graphs where in each synchronous round every vertex - either never changes its label from 1 to 0, and changes its label from 0 to 1 if sufficiently many neighbours have label 1, - or changes its label if sufficiently many neighbours have a different label. In both scenarios the number of neighbours required for a change depends on individual threshold values of the vertices. Our contributions concern computational aspects related to the sets with minimum cardinality of vertices with initial label 1 such that during the process all vertices eventually change their label to 1 and remain with 1 as label. We establish hardness results for the general case and describe efficient algorithms for restricted instances.