Synthesis of fast programs for maximum segment sum problems

It is well-known that a naive algorithm can often be turned into an efficient program by applying appropriate semanticspreserving transformations. This technique has been used to derive programs to solve a variety of maximum-sum programs. One problem with this approach is that each problem variation requires a new set of transformations to be derived. An alternative approach to synthesis combines problem specifications with flexible algorithm theories to derive efficient algorithms. We show how this approach can be implemented in Haskell and applied to solve constraint satisfaction problems. We illustrate this technique by deriving programs for three varieties of maximum-weightsum problem. The derivations of the different programs are similar, and the resulting programs are asymptotically faster in practice than the programs created by transformation. 1

Maximum Marking Problems with Accumulative Weight Functions

Abstract. We present a new derivation of efficient algorithms for a class of optimization problems called maximum marking problems. We extend the class of weight functions used in the specification to allow for weight functions with accumulation, which is particularly useful when the weight of each element depends on adjacent elements. This extension of weight functions enables us to treat more interesting optimization problems such as a variant of the maximum segment sum problem and the fair bonus distribution problem. The complexity of the derived algorithm is linear with respect to the size of the input data