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Section: New Results

Range minimum query

The range minimum query problem consists in finding the minimum value inside any queried range of a preprocessed integer sequence. Several methods exist to compute the minimum in constant time, using almost the theoretical minimal amount of space. Those methods consist in splitting the problem in several subproblems and precomputing the solutions for them.

With Alice Héliou (AMIB Inria team, Saclay), Martine Léonard and Laurent Mouchard (LITIS, Rouen), we designed a new method, which is worse in terms of time complexity [24]. Our solution relies on a totally different concept as previous ones: We only store the values that are local minima. This approach is therefore simple and can, on specific inputs, require much less memory than the general theoretical minimal bound. Moreover the simplicity of the method can be easily adapted to allow updates in the original integer sequence.