@techreport{TR-IC-02-10,
  number = {IC-02-10},
  author = {Y. Kohayakawa and F. K. Miyazawa and
        P.Raghavan and Y. Wakabayashi},
  title = {Multidimensional Cube Packing},
  month = {September},
  year = {2002}, 
  institution = {Institute of Computing, University of Campinas},
  note = {In English, 15 pages.
    \par\selectlanguage{english}\textbf{Abstract}
      We consider the \textit{$d$-dimensional cube packing problem}
      ({\rm {\it d}-CPP}): given a list $L$ of $d$-dim\-en\-sional
      cubes and (an unlimited quantity of) $d$-dimensional
      unit-capacity cubes, called \textit{bins}, find a packing of $L$
      into the minimum number of bins.  We present two approximation
      algorithms for {\rm {\it d}-CPP}, for fixed $d$.  The first
      algorithm has an asymptotic performance bound that can be made
      arbitrarily close to~$2-(1/2)^d$.  The second algorithm is an
      improvement of the first and has an asymptotic performance bound
      that can be made arbitrarily close to~$2-(2/3)^d$.  To our
      knowledge, these results improve the bounds known so far for
      $d=2$ and $d=3$, and are the first results with bounds that are
      not exponential in the dimension.
  }
}