Overlapping subproblems refer to the situation in optimization and algorithm design where the same subproblems are solved multiple times during the computation of a larger problem. This concept is crucial in dynamic programming and combinatorial optimization, as it highlights the efficiency gains that can be achieved by storing and reusing solutions to these subproblems instead of recalculating them each time they are needed. By recognizing and leveraging overlapping subproblems, one can optimize algorithms, particularly in combinatorial extremal problems, enhancing their performance significantly.
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