Faster Funny Matrix Multiplication for the All-Pairs Shortest Paths Problem

Funny Matrix Multiplication (FMM) is a matrix multiplication operation in which the scalar addition and multiplication operations are replaced by the scalar minimization and addition operations, respectively. It is a fundamental computational task for matrices and its applications include the allpairs shortest paths problem. Recently McAuley and Caetano have proposed a new algorithm whose expected computation time is significantly shorter than that of the straightforward FMM computation, while the worst-case time complexity remains unchanged. This paper gives an improved faster FMM algorithm that exploits instruction-level parallelism. By using this new algorithm, the all-pairs shortest paths problem can be solved much more quickly than with the Floyd-Warshall algorithm.