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This paper concerns about mobile ad-hoc wireless networks, but with the added restriction that each radio station has a rectilinear trajectory. The paper focuses on the problem of computing an optimal range assignment for the stations, which allows to perform a broadcast operation from a source station, while the overall energy deployed is minimized. An O(n3 log n)-time algorithm for this problem is presented, under the assumption that all stations have equally sized transmission ranges. However, one proves that the general version of the problem is NP-hard, and it is not approximable within a sub-logarithmic factor (unless P=NP).
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