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Lower bounds for row minima searching

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Bradford,  Phillip Gnassi
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Reinert,  Knut
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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MPI-I-96-1-029.pdf
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Bradford, P. G., & Reinert, K.(1996). Lower bounds for row minima searching (MPI-I-1996-1-029). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-A021-C
Abstract
This paper shows that finding the row minima (maxima) in an $n \times n$ totally monotone matrix in the worst case requires any algorithm to make $3n-5$ comparisons or $4n -5$ matrix accesses. Where the, so called, SMAWK algorithm of Aggarwal {\em et al\/.} finds the row minima in no more than $5n -2 \lg n - 6$ comparisons.