Multiplication Algorithms for Monge Matrices

摘要

In this paper we study algorithms for the max-plus product of Monge matrices. These algorithms use the underlying regularities of the matrices to be faster than the general multiplication algorithm, hence saving time. A non-naive solution is to iterate the SMAWK algorithm. For specific classes there are more efficient algorithms. We present a new multiplication algorithm (MMT), that is efficient for general Monge matrices and also for specific classes. The theoretical and empirical analysis shows that MMT operates in near optimal space and time. Hence we give further insight into an open problem proposed by Landau. The resulting algorithms are relevant for bio-informatics, namely because Monge matrices occur in string alignment problems.