@techreport{AnderssonNilssonHagerupRaman95,
TITLE = {Sorting in linear time?},
AUTHOR = {Andersson, A. and Nilsson, S. and Hagerup, Torben and Raman, Rajeev},
LANGUAGE = {eng},
URL = {http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1995-1-024},
NUMBER = {MPI-I-1995-1-024},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
ADDRESS = {Saarbr{\"u}cken},
YEAR = {1995},
DATE = {1995},
ABSTRACT = {We show that a unit-cost RAM with a word length of $w$ bits can sort $n$ integers in the range $0\Ttwodots 2^w-1$ in $O(n\log\log n)$ time, for arbitrary $w\ge\log n$, a significant improvement over the bound of $O(n\sqrt{\log n})$ achieved by the fusion trees of Fredman and Willard. Provided that $w\ge(\log n)^{2+\epsilon}$ for some fixed $\epsilon>0$, the sorting can even be accomplished in linear expected time with a randomized algorithm. Both of our algorithms parallelize without loss on a unit-cost PRAM with a word length of $w$ bits. The first one yields an algorithm that uses $O(\log n)$ time and\break $O(n\log\log n)$ operations on a deterministic CRCW PRAM. The second one yields an algorithm that uses $O(\log n)$ expected time and $O(n)$ expected operations on a randomized EREW PRAM, provided that $w\ge(\log n)^{2+\epsilon}$ for some fixed $\epsilon>0$. Our deterministic and randomized sequential and parallel algorithms generalize to the lexicographic sorting problem of sorting multiple-precision integers represented in several words.},
TYPE = {Research Report / Max-Planck-Institut für Informatik},
}