Faster deterministic wakeup in multiple access channels

We consider the fundamental problem of waking up n processors sharing a multiple access channel. We assume the weakest model of synchronization, the locally synchronous model, in which no global clock is available: processors have local clocks ticking at the same rate, but each clock starts counting the rounds in the round in which the correspondent processor wakes up. Moreover, the number n   of processors is not known to the processors. We propose a new deterministic algorithm for this problem in time O(n3log3n)O(n3log3n), which improves on the currently best upper bound of O(n4log5n)O(n4log5n).