Stability is an important issue in order to characterize the performance of a network, and it has become a major topic of study in the last decade. Roughly speaking, a communication network system is said to be stable if the number of packets waiting to be delivered (backlog) is finitely bounded at any one time. In this paper, we introduce a new family of combinatorial structures, which we call universally strong selectors, that are used to provide a set of transmission schedules. Making use of these structures, combined with some known queuing policies, we propose a packet-oblivious routing algorithm which is working without using any global topological information, and guarantees stability for certain injection rates. We show that this protocol is asymptotically optimal regarding the injection rate for which stability is guaranteed. Furthermore, we also introduce a packet-oblivious routing algorithm that guarantees stability for higher traffic. This algorithm is optimal regarding the injection rate for which stability is guaranteed. However, it needs to use some global information of the system topology.