Abstract
Given the positions of n sites in a radio network we consider the problem of finding routes between any pair of sites that minimize energy consumption and do not use more than some constant number k of hops. Known exact algorithms for this problem required Ω(n log n) per query pair (p,q). In this paper we relax the exactness requirement and only compute approximate (1 + ε) solutions which allows us to guarantee constant query time using linear space and O(n log n) preprocessing time. The dependence on ε is polynomial in 1/ε.
One tool we employ might be of independent interest: For any pair of points (p,q) ∈ P ⊆ ℤ2 we can report in constant time the cluster pair (A,B) representing (p,q) in a well-separated pair decomposition of P.
This work was partially supported by the IST Programme of the EU under contract number IST-1999-14186 (ALCOM-FT).
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Funke, S., Matijevic, D., Sanders, P. (2003). Approximating Energy Efficient Paths in Wireless Multi-hop Networks. In: Di Battista, G., Zwick, U. (eds) Algorithms - ESA 2003. ESA 2003. Lecture Notes in Computer Science, vol 2832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39658-1_23
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DOI: https://doi.org/10.1007/978-3-540-39658-1_23
Publisher Name: Springer, Berlin, Heidelberg
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