1 research outputs found
A Curious Link Between Prime Numbers, the Maundy Cake Problem and Parallel Sorting
We present new theoretical algorithms that sums the n-ary comparators output
in order to get the permutation indices in order to sort a sequence. By
analysing the parallel ranking algorithm, we found that the special comparators
number of elements it processes divide the number of elements to be sorted.
Using the divide and conquer method, we can express the sorting problem into
summing output of comparators taking a prime number of elements, given that
this prime number divides the initial disordered sequence length. The number of
sums is directly related to the Maundy cake problem. Furthermore, we provide a
new sequence that counts the number of comparators used in the algorithms.Comment: 10 pages, 2 figures, 3 tables, final versio