An Optimal MPC Algorithm for Subunit-Monge Matrix Multiplication, with Applications to LIS

Abstract

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(łog 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(łog^4 n)-round complexity, and matches the best algorithm for computing the (1+ε)-approximation of LIS.