Some complexity results about packet radio networks

It is shown that the decision problem regarding the membership of a given point in the capacity region of a packet radio network (PRN) is NP-complete. The capacity region is the set of all feasible sets of average origin-to-destination traffic rates, where feasibility is defined as the existence of any set of rules for moving the data through the network so that the desired rates are satisfied. The analysis includes a linear programming formulation of TDMA (time-division-multi-access) schemes for PRNs and NP-completeness results for some other related problems. Implicit in the analysis is the optimality of TDMA schemes to achieve a given set of link traffic rates.