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On lower bounds for selecting the median
KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.ORCID iD: 0000-0002-5379-345X
2001 (English)In: SIAM Journal on Discrete Mathematics, ISSN 0895-4801, E-ISSN 1095-7146, Vol. 14, no 3, 299-311 p.Article in journal (Refereed) Published
Abstract [en]

We present a reformulation of the 2n + o(n) lower bound of Bent and John [Proceedings of the 17th Annual A CM Symposium on Theory of Computing, 1985, pp. 213-216] for the number of comparisons needed for selecting the median of n elements. Our reformulation uses a weight function. Apart from giving a more intuitive proof for the lower bound, the new formulation opens up possibilities for improving it. We use the new formulation to show that any pair-forming median finding algorithm, i.e., a median finding algorithm that starts by comparing [n/2] disjoint pairs of elements must perform, in the worst case, at least 2.01n + o(n) comparisons. This provides strong evidence that selecting the median requires at least cn + o(n) comparisons for some c > 2.

Place, publisher, year, edition, pages
2001. Vol. 14, no 3, 299-311 p.
Keyword [en]
median selection, comparison algorithms, lower bounds
Identifiers
URN: urn:nbn:se:kth:diva-20987ISI: 000171372500004OAI: oai:DiVA.org:kth-20987DiVA: diva2:339684
Note
QC 20100525Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved

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Håstad, Johan

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