International audience

A bijection is given between the set of directed column-convex polyominoes on triangular and honeycomb lattices of area n and some families of restricted compositions. This is an analogous result to one given by Deutsch and Prodinger for polyominoes over square lattices. As a byproduct, we deduce new close forms for the number of hexagonal and triangular directed column-convex polyominoes of area n with k columns.

We investigate the problem of computing Completely Independent Spanning Trees (CIST) under a practical approach. We aim to show that despite CISTs are very challenging to exhibit in some networks, they present a real interest in ad-hoc networks and can be computed to enhance the network robustness. We propose an original ILP formulation for CISTs and we show through simulation results on representative network models that several CISTs can be computed when the network density is sufficiently high. These results tend to reinforce the interest of CISTs for various network operations such as robustness, load-balancing, traffic splitting, . . . As an important point, our results show that both the density and the number of nodes have an impact on the number of CISTs that can be found on ad-hoc networks.