In this work, we consider adversarial crash faults of nodes in the network constructors model [Michail and Spirakis, 2016]. We first show that, without further assumptions, the class of graph languages that can be (stably) constructed under crash faults is non-empty but small. When there is a finite upper bound f on the number of faults, we show that it is impossible to construct any non-hereditary graph language and leave as an interesting open problem the hereditary case. On the positive side, by relaxing our requirements we prove that: (i) permitting linear waste enables to construct on (Formula presented) nodes, any graph language that is constructible in the fault-free case, (ii) partial constructibility (i.e., not having to generate all graphs in the language) allows the construction of a large class of graph languages. We then extend the original model with a minimal form of fault notifications, and our main result here is a fault-tolerant universal constructor that requires linear waste in the population. Finally, we show that logarithmic local memories can be exploited for a no-waste fault-tolerant simulation of any such protocol.
CITATION STYLE
Michail, O., Spirakis, P. G., & Theofilatos, M. (2019). Fault Tolerant Network Constructors. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11914 LNCS, pp. 243–255). Springer. https://doi.org/10.1007/978-3-030-34992-9_19
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