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This study addresses the general problem of efficient resource management in wireless networks with arbitrary time-varying topologies. Communication channels are assumed to generally accommodate multiple simultaneous transmissions. In this context, we focus our attention on the problem of distributed transmission power allocation and medium access by links (transmitter-receiver pairs) that require a guaranteed minimum signal-to-interference and noise ratio (SINR) at the receiver for a reliable data transfer. The design constraints for derived solutions consist of (i) a theoretically optimum performance, (ii) minimum complexity in implementation, and (iii) reliable feedback on target SINR feasibility to both active and inactive links. To this end, we propose adaptive algorithms that employ real-time tracking of the spectral radius of the Foschini-Miljanic matrix by means of distributed interference measurements. The algorithm design is characterized by an inherent resistant to the effects of stochastic radio propagation phenomena and an exponential convergence rate - a fact which we prove analytically. Numerical simulations confirm that our approach to admission control reaches the performance upper bounds of comparison algorithms that are based on random access, carrier-sensing, fixed channel probing, controlled power-up, or channel measurements.