Abstract
The selection problem has a long history, with deep roots in concrete complexity theory, and important practical applications. Nevertheless, some very basic questions remain unresolved. Included among these is the exact specification of the worst-case complexity of selecting the third largest of a set of n elements, a problem (originally formulated in terms of tennis tournaments) that dates back to 1883.
Inspired, in part, by the contributions of J. Ian Munro, to the selection problem as well as many other problems in concrete complexity, we revisit a question concerning the complexity of selecting the third largest element. The question was raised, and only partially solved, in the author’s Ph.D. thesis, at a time that marks the beginning of a long friendship with Ian, and research journeys with numerous parallel interests. In this paper, we settle one very specific instance of this question that is interesting, in part, because it constitutes (i) a new counterexample to a natural conjecture about the exact complexity of this problem, and (ii) what the author now believes is the only remaining counterexample.
The author hopes, in this modest way, to reflect his deep admiration for Ian’s many contributions to the theory, practice and appreciation of algorithm design and analysis.
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Kirkpatrick, D. (2013). Closing a Long-Standing Complexity Gap for Selection: V 3(42) = 50. In: Brodnik, A., López-Ortiz, A., Raman, V., Viola, A. (eds) Space-Efficient Data Structures, Streams, and Algorithms. Lecture Notes in Computer Science, vol 8066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40273-9_6
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DOI: https://doi.org/10.1007/978-3-642-40273-9_6
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