## Minimum-energy multicast in mobile ad hoc networks using network coding (2005)

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Venue: | IEEE Trans. Commun |

Citations: | 86 - 2 self |

### BibTeX

@ARTICLE{Wu05minimum-energymulticast,

author = {Yunnan Wu and Student Member and Philip A. Chou and Sun-yuan Kung},

title = {Minimum-energy multicast in mobile ad hoc networks using network coding},

journal = {IEEE Trans. Commun},

year = {2005},

volume = {53},

pages = {1906--1918}

}

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### Abstract

Abstract — The minimum energy required to transmit a bit of information through a network characterizes the most economical way to communicate in a network. In this paper, we show that under a layered model of wireless networks, the minimum energyper-bit for multicasting in a mobile ad hoc network can be found by a linear program; the minimum energy-per-bit can be attained by performing network coding. Compared with conventional routing solutions, network coding not only promises a potentially lower energy-per-bit, but also enables the optimal solution to be found in polynomial time, in sharp contrast with the NPhardness of constructing the minimum-energy multicast tree as the optimal routing solution. We further show that the minimum energy multicast formulation is equivalent to a cost minimization with linear edge-based pricing, where the edge prices are the energy-per-bits of the corresponding physical broadcast links. This paper also investigates minimum energy multicasting with routing. Due to the linearity of the pricing scheme, the minimum energy-per-bit for routing is achievable by using a single distribution tree. A characterization of the admissible rate region for routing with a single tree is presented. The minimum energy-per-bit for multicasting with routing is found by an integer linear program. We show that the relaxation of this integer linear program, studied earlier in the Steiner tree literature, can now be interpreted as the optimization for minimum energy multicasting with network coding. In short, this paper presents a unifying study of minimum energy multicasting with network coding and routing. Index Terms — Network coding, routing, multicast, Steiner tree, wireless ad hoc networks, energy efficiency, mobility.