Januszewski, Janusz; Lassak, Marek; Rote, Günter; Woeginger, Gerhard On-line \(q\)-adic covering by the method of the \(n\)-th segment and its application to on-line covering by cubes. (English) Zbl 0863.52010 Beitr. Algebra Geom. 37, No. 1, 51-65 (1996). The authors’ abstract: “We prove that in Euclidean \(d\)-space every sequence of cubes with total volume \(2^d+3\) is able to cover on-line the unit cube.The proof is based on an on-line \(q\)-adic method of covering the unit segment by segments of lengths of the form \(q^{-r}\), where \(q\geq 2\) and \(r \geq 1\) are integers. The fact that this method is \(q\)-adic means that every segment has to be placed in such a way that both end-points are at points that are multiples of the length of the segment”. Reviewer: H.-D.Hecker (Jena) Cited in 1 Document MSC: 52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry) 68W10 Parallel algorithms in computer science Keywords:on-line covering; Euclidean \(d\)-space; \(q\)-adic; sequence of cubes; unit cube PDFBibTeX XMLCite \textit{J. Januszewski} et al., Beitr. Algebra Geom. 37, No. 1, 51--65 (1996; Zbl 0863.52010) Full Text: EuDML EMIS