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Theoretical Computer Science
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We present two merging algorithms on a single-channel single-hop radio network without collision detection. The simpler of these algorithms merges two sorted sequences of length n in time 4n with energetic cost for each station $\approx {\rm lg} {\it n}$. The energetic cost of broadcasting is constant. This yields the merge-sort for n elements in time 2nlg n, where the energetic cost for each station is $\frac{1}{2}{\rm lg}^{2}{\it n}+\frac{7}{2} {\rm lg}{\it n}$ (the energetic cost of broadcasting is only 2 lg n), which seems to be suitable for practical applications due to its simplicity and low constants. We also present algorithm for merging in time O(nlg*n) with energetic cost O(lg* n).