Byzantine approximate agreement on chordal graphs and cycle-free semilattices is solvable in O(log N) asynchronous rounds when n > (ω+1)f, and synchronous exact convex consensus has tight resilience Θ(f).
We consider the exact variant of the abstract approximate agreement problem, where the agreement constraint is replaced by|Y| = 1
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Byzantine Approximate Agreement on Graphs
Byzantine approximate agreement on chordal graphs and cycle-free semilattices is solvable in O(log N) asynchronous rounds when n > (ω+1)f, and synchronous exact convex consensus has tight resilience Θ(f).