  Studying on networked systems, in which a communication between nodes is
functional if their distance under a given metric is lower than a pre-defined
threshold, has received significant attention recently. In this work, we
propose a metric to measure network resilience on guaranteeing the pre-defined
performance constraint. This metric is investigated under an optimization
problem, namely \textbf{Length-bounded Paths Interdiction in Continuous Domain}
(cLPI), which aims to identify a minimum set of nodes whose changes cause
routing paths between nodes become undesirable for the network service.
  We show the problem is NP-hard and propose a framework by designing two
oracles, \textit{Threshold Blocking} (TB) and \textit{Critical Path Listing}
(CPL), which communicate back and forth to construct a feasible solution to
cLPI with theoretical bicriteria approximation guarantees. Based on this
framework, we propose two solutions for each oracle. Each combination of one
solution to \tb and one solution to \cpl gives us a solution to cLPI. The
bicriteria guarantee of our algorithms allows us to control the solutions's
trade-off between the returned size and the performance accuracy. New insights
into the advantages of each solution are further discussed via experimental
analysis.
