Abstract
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′, such that for any two nodes u and v, there exists a path from u to v in G′, 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).
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A preliminary version of this paper appears in Proceedings of the 29th IEEE International Conference on Computer Communications, 2010.
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Abu-Affash, A.K., Aschner, R., Carmi, P. et al. Minimum power energy spanners in wireless ad hoc networks. Wireless Netw 17, 1251–1258 (2011). https://doi.org/10.1007/s11276-011-0346-7
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DOI: https://doi.org/10.1007/s11276-011-0346-7