• Corpus ID: 8111215

Refining the Analysis of Divide and Conquer: How and When

  title={Refining the Analysis of Divide and Conquer: How and When},
  author={J{\'e}r{\'e}my F{\'e}lix Barbay and Carlos Ochoa and Pablo P{\'e}rez-Lantero},
Divide-and-conquer is a central paradigm for the design of algorithms, through which some fundamental computational problems, such as sorting arrays and computing convex hulls, are solved in optimal time within $\Theta(n\log{n})$ in the worst case over instances of size $n$. A finer analysis of those problems yields complexities within $O(n(1 + \mathcal{H}(n_1, \dots, n_k))) \subseteq O(n(1{+}\log{k})) \subseteq O(n\log{n})$ in the worst case over all instances of size $n$ composed of $k$ "easy… 

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