Abstract:Rounding has proven to be a fundamental tool in theoretical computer science. By observing that rounding and partitioning of R d are equivalent, we introduce the following natural partition problem which we call the secluded hypercube partition problem: Given k ∈ N (ideally small) and > 0 (ideally large), is there a partition of R d with unit hypercubes such that for every point p ∈ R d , its closed -neighborhood (in the ∞ norm) intersects at most k hypercubes?We undertake a comprehensive study of this partiti… Show more
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