Proceedings of the twenty-ninth annual symposium on Computational geometry
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A power assignment is an assignment of transmission power to each of the nodes of a wireless network, so that the induced communication graph has some desired properties. The cost of a power assignment is the sum of the powers. The energy of a transmission path from node u to node v is the sum of the squares of the distances between adjacent nodes along the path. For a constant t 1, an energy t-spanner is a graph G驴, such that for any two nodes u and v, there exists a path from u to v in G驴, whose energy is at most t times the energy of a minimum-energy path from u to v in the complete Euclidean graph. In this paper, we study the problem of finding a power assignment, such that (1) its induced communication graph is a `good' energy spanner, and (2) its cost is `low'. We show that for any constant t 1, one can find a power assignment, such that its induced communication graph is an energy t-spanner, and its cost is bounded by some constant times the cost of an optimal power assignment (where the sole requirement is strong connectivity of the induced communication graph). This is a significant improvement over the previous result due to Shpungin and Segal in Proceedings of 28th IEEE INFOCOM, pp 163---171, (2009).