  We consider a strategic network monitoring problem involving the operator of
a networked system and an attacker. The operator aims to randomize the
placement of multiple protected sensors to monitor and protect components that
are vulnerable to attacks. We account for the heterogeneity in the components'
security levels and formulate a large-scale maximin optimization problem. After
analyzing its structure, we propose a three-step approach to approximately
solve the problem. First, we solve a generalized covering set problem and run a
combinatorial algorithm to compute an approximate solution. Then, we compute
approximation bounds by solving a nonlinear set packing problem. To evaluate
our solution approach, we implement two classical solution methods based on
column generation and multiplicative weights updates, and test them on
real-world water distribution and power systems. Our numerical analysis shows
that our solution method outperforms the classical methods on large-scale
networks, as it efficiently generates solutions that achieve a close to optimal
performance and that are simple to implement in practice.
