Algorithms for channel assignment in mobile wireless networks using temporal coloring

We model the problem of channel assignment in mobile networks as one of temporal coloring (T-coloring), that is, coloring a time-varying graph. In order to capture the impact of channel re-assignments due to mobility, we model the cost of coloring as C + αA, where C is the total number of colors used and A is the total number of color changes, and α is a user-selectable parameter reflecting the relative penalty of channel usage and re-assignments. Using these models, we present several novel algorithms for temporal coloring. We begin by analyzing two simple algorithms called SNAP and SMASH that take diametrically opposite positions on colors vs re-assignments, and provide theoretical results on the ranges of α in which one outperforms the other, both for arbitrary and random time-varying graphs. We then present six more algorithms that build upon each of SNAP and SMASH in different ways. Simulations on random geometric graphs with random waypoint mobility show that the relative cost of the algorithms depends upon the value of α and the transmission range, and we identify precise values at which the crossovers happen.