Abstract
The paper studies the problem of computing a minimal energy cost range assignment in a ad-hoc wireless network which allows a station s to perform a broadcast operation in at most h hops. The general version of the problem (i.e., when transmission costs are arbitrary) is known to be log-APX hard even for h=2. The current paper considers the well-studied real case in which n stations are located on the plane and the cost to transmit from station i to station j is proportional to the α-th power of the distance between station i and j, where α is any positive constant. A polynomial-time algorithm is presented for finding an optimal range assignment to perform a 2-hop broadcast from a given source station. The algorithm relies on dynamic programming and operates in (worst-case) time O(n 7). Then, a polynomial-time approximation scheme (PTAS) is provided for the above problem for any fixed h ≥ 1. For fixed h ≥ 1 and ε> 0, the PTAS has time complexity O(n μ) where \(\mu = O((\alpha 2^{\alpha}h^{\alpha}/\epsilon)^{\alpha^h})\).
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Ambühl, C. et al. (2004). Efficient Algorithms for Low-Energy Bounded-Hop Broadcast in Ad-Hoc Wireless Networks. In: Diekert, V., Habib, M. (eds) STACS 2004. STACS 2004. Lecture Notes in Computer Science, vol 2996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24749-4_37
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DOI: https://doi.org/10.1007/978-3-540-24749-4_37
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