Abstract
Given a set A of distinct 0–1 vectors and a vector u in A, how many bits of u must we know in order to distinguish it from the other vectors in A? Such a set of bits is a witness for the fact that u ∉ A - {u}. In this chapter we will give some basic estimates on the size of these witnesses. We will also consider a related problem of how to isolate an object within a given universum according to its weight. Finally, we will describe the so-called “dictator paradox” saying that, if the society fulfills some simple “democracy axioms,” then there will always be an individual (a dictator?) whose options prevail against all options.
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© 2001 Springer-Verlag Berlin Heidelberg
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Jukna, S. (2001). Witness Sets and Isolation. In: Extremal Combinatorics. Texts in Theoretical Computer Science. An EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04650-0_14
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DOI: https://doi.org/10.1007/978-3-662-04650-0_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08559-8
Online ISBN: 978-3-662-04650-0
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