Distributed Long-Lived List Colouring: How to Dynamically Allocate Frequencies in Cellular Networks

To avoid signal interference in mobile communication it is necessary that the frequen cies used for communication within each cells are allocated so that no signal interference occurs with neighbouring cells We model this channel allocation problem as a generalised list colouring problem and we show how to analytically measure and provide worst case guarantees regarding request satis ability To the best of our knowledge this has not been done before and gives a new perspective to the problem as well as a clear direction for further investigation We propose distributed approaches for solving the problem which are able to adapt fast to temporal variations in channel demands in di erent cells as well as to cope with crash failures by limiting the failure locality the size of the network that can be a ected by a faulty station in terms of the distance from that station Our rst approach is inspired by a relatively recent theorem relating graph colourings and orientations it achieves the equivalent of the best known sequentially achievable upper bound for request satis ability implied by the theorem It also employs a powerful synchronisation mechanism to achieve worst case response time that depends only on the degree of the signal interference graph and failure locality Our second proposal is a rst approach towards exploring what bound in request satis ability is achievable without the use of extra synchronisation by employing ran domisation in frequency choices in only one round of communication a base station can expect to pick f frequencies where f is the size of the list at the node the failure locality of this solution is only