Summary: Tech. report, Lund University, 1994.
Blasting Past Fusion Trees
Arne Andersson \Lambda Stefan Nilsson \Lambda Torben Hagerup y
10 October 1994
We present an O(n log log n) worstcase time algorithm for sorting arbi
trary integers, a significant improvement over the bound achieved by the
fusion tree of Fredman and Willard.
Model of computation
We will consider a unit cost random access machine, RAM, with word length
w and a memory composed of 2 w words. The instruction set includes addition,
subtraction, comparison, unrestricted shift and the bitwise boolean operations
AND and OR.
We study the problem of sorting n integers in the range 1::2 b on a RAM. We say
that T (n; b) ź f(n) if there exists an algorithm with worstcase time complexity
f(n) that solves this sorting problem. The assertion that T (n; b 2
) ź f(n) )
T (n; b 1
) ź f(n) will be abbreviated as T (n; b 1