Optimal Byzantine attacks on distributed detection in tree-based topologies

This paper considers the problem of optimal Byzantine attacks or data falsification attacks on distributed detection mechanism in tree-based topologies. First, we show that when more than a certain fraction of individual node decisions are falsified, the decision fusion scheme becomes completely incapable. Second, under the assumption that there is a cost associated with attacking each node (which represent resources invested in capturing a node or cloning a node in some cases), we address the problem of minimum cost Byzantine attacks and formulate it as the bounded knapsack problem (BKP). An algorithm to solve our problem in polynomial time is presented. Numerical results provide insights into our solution.