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Submodularity and Optimality of Fusion Rules in Balanced Binary Relay Trees
We study the distributed detection problem in a balanced binary relay tree,
where the leaves of the tree are sensors generating binary messages. The root
of the tree is a fusion center that makes the overall decision. Every other
node in the tree is a fusion node that fuses two binary messages from its child
nodes into a new binary message and sends it to the parent node at the next
level. We assume that the fusion nodes at the same level use the same fusion
rule. We call a string of fusion rules used at different levels a fusion
strategy. We consider the problem of finding a fusion strategy that maximizes
the reduction in the total error probability between the sensors and the fusion
center. We formulate this problem as a deterministic dynamic program and
express the solution in terms of Bellman's equations. We introduce the notion
of stringsubmodularity and show that the reduction in the total error
probability is a stringsubmodular function. Consequentially, we show that the
greedy strategy, which only maximizes the level-wise reduction in the total
error probability, is within a factor of the optimal strategy in terms of
reduction in the total error probability
A multi-objective framework for the optimisation of life-cycle costs of wind turbines
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