We present an $O(1)$-round fully-scalable deterministic massively parallel algorithm for computing the min-plus matrix multiplication of unit-Monge matrices. We use this to derive a $O(\log n)$-round fully-scalable massively parallel algorithm for solving the exact longest increasing subsequence (LIS) problem. For a fully-scalable MPC regime, this result substantially improves the previously known algorithm of $O(\log^4 n)$-round complexity, and matches the best algorithm for computing the $(1+\epsilon)$-approximation of LIS.

翻译：我们提出了一种$O(1)$轮完全可扩展的确定性大规模并行算法，用于计算单元-蒙日矩阵的最小加矩阵乘法。利用该算法，我们推导出一种$O(\log n)$轮完全可扩展的大规模并行算法，用于求解精确的最长递增子序列（LIS）问题。在完全可扩展的MPC机制下，该结果显著改进了先前已知的$O(\log^4 n)$轮复杂度算法，并达到了与计算LIS的$(1+\epsilon)$近似最佳算法相同的性能。