Before revision:  Consider a metric space (X, d_X ]  ), a graph H over X is a \vartheta-reliable t-spanner if, for every set of failed vertices B\subset X, there is a superset B^+\supseteq B such that the induced subgraph H }} [ X\setminus B ] preserves all the distances between points in X\setminus B^+ up to a stretch factor t, while the expected size of B^+ is as most (1+\vartheta)|B|.
After revision:  Consider a metric space (X, d_X ] recently developed locality-sensitive ordering (LSO ), a graph H over X is a \vartheta-reliable t-spanner if, for every set of failed vertices B\subset X, there is a superset B^+\supseteq B such that the induced subgraph H }} [ X\setminus B ] preserves all the distances between points in X\setminus B^+ up to a stretch factor t, while the expected size of B^+ is as most (1+\vartheta)|B|.