This paper presents a new form of consensus that allows nodes to agree locally on the extent of crashed regions in networks of arbitrary size. One key property of our algorithm is that it shows local complexity, i.e. its cost is independent of the size of the complete system, and only depends on the shape and extent of the crashed region to be agreed upon. In this paper, we motivate the need for such an algorithm, formally define this new consensus problem, propose a fault-tolerant solution, and prove its correctness.
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