Algorithms for Implementing Fair Wireless Power Allocations

We describe algorithms for fairly allocating power among wireless devices sharing a multiple access channel. This problem can be formulated as one of finding a representation of a point in a contra-polymatroid as a convex combination of a small number of its extreme points. We show that this problem is solvable in polynomial time and then describe a fast algorithms based on the Dantzig-Wolfe decomposition. We also describe a faster algorithm when rates are clustered which combines the Dantzig-Wolfe decomposition with a greedy algorithm. (We note that this greedy algorithm solves an interesting covering problem with balls in the L metric.) We also present new algorithms for computing several fair allocations.