Efficient Multihop Broadcast with Distributed Protocol Evolution

Abstract

In this paper we address the minimum-energy broadcast problem. To increase the energy efficiency, we allow nodes that are out of the transmission range of a transmitter to collect the energy of unreliably received overheard signals. As a message is forwarded through the network, a node will have multiple opportunities to reliably receive the message by collecting energy during each retransmission. We refer to this strategy as accu-mulative broadcast. Under the assumption that the nodes reliably forward messages, we formulate the minimum-energy accumulative broadcast problem. We present a solution employing two subproblems. First, we identify the ordering in which nodes should transmit. Second, we determine the optimum power levels for that ordering. While the second subproblem can be solved by means of linear programming, the ordering subproblem is found to be NP-complete. We devise a heuristic algorithm to find a good ordering and evaluate the performance of the algorithm. Preliminary results show the performance of the heuristic algorithm is generally close to the optimum solution. Results also show a significant improvement compared to the well known BIP algorithm for constructing an energy-efficient broadcast tree.

How many times can a function be iterated?

“…Our optimism decreased when T. Wiandt [15] showed us a simple situation (see Example 4.3) where X and C are compact and connected but only four iterations are possible. That example showed us that further requirements on f , C, X were needed in order to perform further iterations of f .…”