Abstract
We show how to select an item with the majority color from n two-colored items, given access to the items only through an oracle that returns the discrepancy of subsets of k items. We use \(n/\lfloor \tfrac{k}{2}\rfloor +O(k)\) queries, improving a previous method by De Marco and Kranakis that used \(n-k+k^2/2\) queries. We also prove a lower bound of \({n/(k-1)-O(n^{1/3})}\) on the number of queries needed, improving a lower bound of \(\lfloor n/k\rfloor \) by De Marco and Kranakis.
David Eppstein was supported in part by NSF grant CCF-1228639.
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- 1.
There is a bug in their method for odd k, in Case 1 of Theorem 4.1, when \(i=\lfloor k/2\rfloor \).
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Eppstein, D., Hirschberg, D.S. (2016). From Discrepancy to Majority. In: Kranakis, E., Navarro, G., Chávez, E. (eds) LATIN 2016: Theoretical Informatics. LATIN 2016. Lecture Notes in Computer Science(), vol 9644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49529-2_29
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DOI: https://doi.org/10.1007/978-3-662-49529-2_29
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