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キーワード:
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要旨:
We show how to generate randomized roundings of rational vectors that satisfy
hard cardinality constraints and allow large deviations bounds. This improves
and extends earlier results by Srinivasan (FOCS 2001), Gandhi et al. (FOCS
2002) and the author (STACS 2006). Roughly speaking, we show that also for
rounding arbitrary rational vectors randomly or deterministically, it suffices
to understand the problem for vectors (which typically is much easier). So far,
this was only known for vectors with entries in , ℓ ∈ ℕ.
To prove the general case, we exhibit a number of results of independent
interest, in particular, a quite useful lemma on negatively correlated random
variables, an extension of de Werra’s (RAIRO 1971) coloring result for
unimodular hypergraphs and a sufficient condition for a unimodular hypergraph
to have a perfectly balanced non-trivial partial coloring.
We also show a new solution for the general derandomization problem for
rational matrices.
