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A general lower bound is presented for the complexity of comparison-based algorithms that 7~" determine rank respecting selections from, or partitions of, arbitrary totally ordered sets. The lower bound :" is constructed by a reduction method that, unlike most earlier results, does not appeal (at least directly) to an adversary argument. The bound equals or improves all known general lower bounds for these problen~ in all cases, unifying results for such special cases as determining the second largest element and determining the median.

A Unified Lower Bound for Selection and Set Partitioning Problems