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We present an improved algorithm to wake up a multi-hop ad-hoc radio network. The goal is to have all the nodes activated, when some of them may wake up spontaneously at arbitrary times and the remaining nodes need to be awoken by the already active ones. The best previously known wake-up algorithm was given by Chrobak, Gasieniec and Kowalski [11], and operated in time O(n^5/3 log n), where n is the number of nodes. We give an algorithm with the running time O(n^3/2 log n). This also yields better algorithms for other synchronization-type primitives, like leader election and local-clocks synchronization, each with a time performance that differs from that of wake-up by an extra factor of O(log n) only, and improves the best previously known method for the problem by a factor of n^1/6. A wake-up algorithm is a schedule of transmissions for each node. It can be represented as a collection of binary sequences …