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Algorithm: Treat the rows as sorted elements of a sequence and perform mergesort on the elements.
Work:
Span:
Proof of Work and Span: The merge operation is linear work, so the work of merge at the root node is
. The work at the lowest level of the call tree is
. Thus, work of the algorithm is the same at all levels. By the brick method (i.e. Master's Theorem), overall work must be
. Algorithm has
at the root and
span at the lowest level of the call tree, so it is root-dominated in terms of span. Thus, span is
.
- narainsk March 11, 2015