The claimed Θ(n^{1+1/(2^r-1)}k^{1-1/(2^r-1)}) characterization of r-round partition learning holds only for k≥r+2 and is contradicted for k=3, r=2.
Cut query algorithms with star contraction
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Learning Partitions with Optimal Query and Round Complexities
The claimed Θ(n^{1+1/(2^r-1)}k^{1-1/(2^r-1)}) characterization of r-round partition learning holds only for k≥r+2 and is contradicted for k=3, r=2.