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Theoretical Computer Science
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This paper presents an efficient randomized emulation of single-hop radio network with collision detection on multi-hop radio network without collision detection. Each step of the single-hop network is emulated by O((D + log n/ε) log Δ) rounds of multi-hop network and succeeds with probability ≥ 1 - ε. (n is the number of processors, D the diameter and Δ the maximum degree). It is shown how to emulate any polynomial algorithm such that the probability of failure remains ≥ ε. A consequence of the emulation is an efficient randomized algorithm for choosing a leader in a multi-hop network.