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arXiv · 1512.06488

From Discrepancy to Majority

David Eppstein·Daniel S. Hirschberg
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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.

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David Eppstein, Daniel S. Hirschberg. 2015-12-21. From Discrepancy to Majority. https://doi.org/10.1007/s00453-017-0303-7

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