Abstract
Ad-hoc wireless networks have no wired infrastructure. Instead, they consist of a collection of radio stations S={1,2,...,n} deployed in a given region and connected by wireless links. Each station is assigned a transmission range, and a station t can correctly receive the transmission of another station s if and only if t is within the range of s. The overall range assignment, r: S→R + , determines a (directed) transmission graph G r . The transmission range of a station depends on the energy invested by the station. In particular, the power P s required by a station s to correctly transmit data to another station t must satisfy the inequality \(P_s \ge {\tt dist}(s,t)^{\alpha}\), where dist(s,t) is the Euclidean distance between s and t and α≥1 is the distance-power gradient. The value of α may vary from 1 to more than 6 depending on the environment conditions at the location of the network (see [16]).
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Peleg, D. (2006). Recent Advances on Approximation Algorithms for Minimum Energy Range Assignment Problems in Ad-Hoc Wireless Networks. In: Erlebach, T. (eds) Combinatorial and Algorithmic Aspects of Networking. CAAN 2006. Lecture Notes in Computer Science, vol 4235. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11922377_1
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