Minimum-Energy Broadcast with Few Senders

Broadcasting a message from a given source node to all other nodes is a fundamental task during the operation of a wireless network. In many application scenarios the network nodes have only a limited energy supply, hence minimizing the energy consumption of any communication task prolongs the lifetime of the network. During a broadcast operation using intermediate nodes to relay messages within the network might decrease the overall energy consumption since the cost of transmitting a message grows super-linearly with the distance. On the other hand using too many intermediate nodes during a broadcast operation increases both latency as well as the chances that some transmission could not properly received (e.g. due to interference). In this paper we consider a constrained broadcast operation, where a source node wants to send a message to all other nodes in the network but at most k nodes are allowed to participate actively, i.e. transmit the message. Restricting the number of transmitting nodes helps in reducing interference, latency and increasing reliability of the broadcast operation, of course at the cost of a slightly higher energy consumption. For the case of network nodes embedded in the Euclidean plane we provide a (1+Ɛ)- approximation algorithm which runs in time linear in n and polynomial in 1/Ɛ but with an exponential dependence on k. As an alternative we therefore also provide an O(1)-approximation whose running time is linear in n and polynomial in k. The existence of a (1 + Ɛ)-approximation algorithm is in stark contrast to the unconstrained broadcast problem where even in the Euclidean plane no algorithm with approximation factor better than 6 is known so far.

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