the colorful paths and rainbow paths have been considered by severalauthors.a colorful directed path in a digraph $g$ is a directed path with $chi(g)$ vertices whose colors are different. a $v$-colorful directed path is such a directed path, starting from $v$. we prove that for a given $3$-regular triangle-free digraph $g$ determining whether there is a proper $chi(g)$-coloring of $g$such that ...

due to its simplicity radix-2 is a popular algorithm to implement fast fourier transform. radix - 2 p algorithms have the same order of computational complexity as higher radices algorithms, but still retain the simplicity of radix-2 . by defining a new concept, twiddle factor template , in this paper we propose a method for exact calculation of multiplicative complexity for radix-2 p algorithm...

In the biclique attack, a shorter biclique usually results in less data complexity, but at the expense of more computational complexity. The early abort technique can be used in partial matching part of the biclique attack in order to slightly reduce the computations. In this paper, we make use of this technique, but instead of slight improvement in the computational complexity, we keep the amo...