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Bardales Roncalla, Wilfredo; Laber, Eduardo Sany (Advisor). On the Lower Bound for the Maximum Consecutive Sub-Sums Problem. Rio de Janeiro, 2013. 60p. MSc. Dissertation — Departamento de Informática, Pontif́ıcia Universidade Católica do Rio de Janeiro. The Maximum Consecutive Subsums Problem (MCSP) arises in scenarios of both theoretical and practical interest, for example, approximate pattern matching, protein identification and analysis of statistical data to cite a few. Given a sequence of n non-negative real numbers, The MCSP asks for the computation of the maximum consecutive sums of lengths 1 through n. Since trivial implementations allow to compute the maximum for a fixed length value, it follows that there exists a naive quadratic procedure to solve the MCSP. Notwithstanding the effort devoted to the problem, no algorithm is known which is significantly better than the naive solution. Therefore, a natural question is whether there exists a superlinear lower bound for the MCSP. In this work we report our research in the direction of proving such a lower bound.

ON THE LOWER BOUND FOR THE MAXIMUM CONSECUTIVE SUB-SUMS PROBLEM