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Novel algorithms for the network lifetime problem in wireless settings

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Abstract

One of the major concerns in wireless ad-hoc networks design is energy efficiency. Wireless devices are typically equipped with a limited energy supply sufficient only for a limited amount of time which is reversely proportional to the transmission power of the device. The network lifetime is defined as the time the first device runs out of its initial energy charge. In this paper we study the maximum network lifetime problem for broadcast and data gathering in wireless settings. We provide polynomial time approximation algorithms, with guaranteed performance bounds while considering omnidirectional and unidirectional transmissions. We also consider an extended variant of the maximum lifetime problem, which simultaneously satisfies additional constraints, such as bounded hop-diameter and degree of the routing tree, and minimizing the total energy used in a single transmission. Finally, we evaluate the performance of some of our algorithms through simulations.

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Notes

  1. The packets are assumed to be unit size.

  2. Multicast is a more general case of broadcast. A source node is required to transmit to a set of nodes; unicast is more specific, a source node is required to transmit to a single node.

  3. The Cauchy-Schwartz inequality states that for any \(x_1,x_2,\ldots,x_l \in {\mathbb{R}}\), \(\left(\sum^k_{l=1}x_l\right)^2 \le k\left(\sum^k_{l=1}x_l^2\right)\).

  4. Though graph G′ V does not necessarily have uniform weights, nevertheless we use this scaling in future developments.

  5. Instead of adding k − 1 copies of an edge, we may assign to every edge capacity k, and consider the corresponding ”capacited” problems; this will give a polynomial algorithm, rather than a pseudo-polynomial one. For simplicity of exposition, we will present the algorithm in terms of multigraphs, but it can be easily adjusted to the terms of capacitated graphs.

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Authors and Affiliations

  1. Department of Computer Science, Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel

    Michael Elkin

  2. Department of Communication Systems Engineering, Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel

    Yuval Lando & Michael Segal

  3. Computer Science Division, The Open University of Israel, 43107, Raanana, Israel

    Zeev Nutov

  4. Department of Computer Science, University of Calgary, Calgary, AB, T2N 1N4, Canada

    Hanan Shpungin

Authors
  1. Michael Elkin
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  2. Yuval Lando
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  3. Zeev Nutov
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  4. Michael Segal
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  5. Hanan Shpungin
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Corresponding author

Correspondence to Hanan Shpungin.

Additional information

A preliminary version of this extended paper has appeared in ADHOC-NOW’08.

Michael Elkin—Supported by the Israeli Academy of Science (grant #483/06).

Michael Segal—Supported by REMON (4G networking) consortium.

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Elkin, M., Lando, Y., Nutov, Z. et al. Novel algorithms for the network lifetime problem in wireless settings. Wireless Netw 17, 397–410 (2011). https://doi.org/10.1007/s11276-010-0287-6

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  • DOI: https://doi.org/10.1007/s11276-010-0287-6

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