MATHEMATICAL ENGINEERING TECHNICAL REPORTS Solving Maximum Weighted-sum Problems for Free

Efficient algorithms are necessary for solving problems effectively. However, efficient algorithms are hard to develop, implement, and maintain. Therefore, it has been very difficult for those with little algorithmic knowledge to solve their problems based on efficient algorithms. In this paper, we introduce a way to develop efficient algorithms for finding optimal sequences, especially sequences of the maximum weighted sum. we formalize derivation of efficient algorithms by shortcut fusion, which is a program transformation known to be suitable for mechanization, and propose a set of laws that is helpful to derive well-structured consumers that are necessary for utilizing our shortcut fusion laws. Moreover, we introduce a library for obtaining optimal lists. The library consists of several functions useful for describing lists satisfying our requirements; moreover, the library consists of program transformation rules so that programs written by our library will be improved automatically into ones based on efficient algorithms.