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Given a sequence of n numbers, the Maximum Consecutive Subsums Problem (MCSP)asks for the maximum consecutive sum of lengths l for each l = 1,...,n. Noalgorithm is known for this problem which is significantly better than thenaive quadratic solution. Nor a super linear lower bound is known. The bestknown bound for the MCSP is based on the the computation of the(min,+)-convolution, another problem for which neither an O(n^{2-{\epsilon}})upper bound is known nor a super linear lower bound. We show that the twoproblems are in fact computationally equivalent by providing linear reductionsbetween them. Then, we concentrate on the problem of finding super linear lowerbounds and provide empirical evidence for an {\Omega}(nlogn) lower bounds forboth problems in the decision tree model.

Searching for a superlinear lower bounds for the Maximum Consecutive Subsums Problem and the (min,+)-convolution