A polylog-time and $O(n\sqrt\lg n)$-work parallel algorithm for finding the row minima in totally monotone matrices

We give a parallel algorithm for computing all row minima in a totally monotone $n\times n$ matrix which is simpler and more work efficient than previous polylog-time algorithms. It runs in $O(\lg n \lg\lg n)$ time doing $O(n\sqrt{\lg n})$ work on a {\sf CRCW}, in $O(\lg n (\lg\lg n)^2)$ time doing $O(n\sqrt{\lg n})$ work on a {\sf CREW}, and in $O(\lg n\sqrt{\lg n \lg\lg n})$ time doing $O(n\sqrt{\lg n\lg\lg n})$ work on an {\sf EREW}