The LS (Look and Say) derivative of a word is obtained by writing the number of consecutive equal letters when the word is spelled from left to right. For example, LS( 1 1 2 3 3) = 2 1 1 2 2 3 (two 1, one 2, two 3). We start the study of the behaviour of binary words generated by morphisms under the LS operator, focusing in particular on the Fibonacci word.
Ce travail consiste à étudier les comportements des marches sur les arbres homogènes suivant la suite engendrée par une substitution. Dans la première partie, on étudie d’abord les marches sans orientation sur et on détermine complètement, d’après les propriétés combinatoires de la substitution, les conditions assurant que les marches sont bornées, récurrentes ou transientes. Comme corollaire, on obtient le comportement asymptotique des sommes partielles des coefficients de la suite substitutive....
We provide an algorithm for listing all minimal 2-dominating sets of a tree of order n in time 𝒪(1.3248n). This implies that every tree has at most 1.3248n minimal 2-dominating sets. We also show that this bound is tight.
We present briefly some results we obtained with known methods to solve minimum cost tension problems, comparing their performance on non-specific graphs and on series-parallel graphs. These graphs are shown to be of interest to approximate many tension problems, like synchronization in hypermedia documents. We propose a new aggregation method to solve the minimum convex piecewise linear cost tension problem on series-parallel graphs in operations.
We present briefly some results we obtained with known methods to solve minimum cost tension problems, comparing their performance on non-specific graphs and on series-parallel graphs. These graphs are shown to be of interest to approximate many tension problems, like synchronization in hypermedia documents. We propose a new aggregation method to solve the minimum convex piecewise linear cost tension problem on series-parallel graphs in O(m3) operations.
A vertex k-ranking of a simple graph is a coloring of its vertices with k colors in such a way that each path connecting two vertices of the same color contains a vertex with a bigger color. Consider the minimum vertex ranking spanning tree (MVRST) problem where the goal is to find a spanning tree of a given graph G which has a vertex ranking using the minimal number of colors over vertex rankings of all spanning trees of G. K. Miyata et al. proved in [NP-hardness proof and an approximation algorithm...