关键词：通信下界；并行算法；矩阵乘法算法
摘 要：In this thesis, we develop both new communication lower bounds and new algorithms, tightening (and in many cases closing) the gap between best known lower bound and best known algorithm (or upper bound). We consider both sequential and parallel algorithms, and we asses both classical and fast algorithms (e.g., Strassen's matrix multiplication algorithm).