Compute dependable spanners under pair-specific edge failure probabilities

Develop an algorithm to construct a dependable spanner of near-optimal size for a point set in R^d when the failure probability is specified explicitly for every pair of points (i.e., each potential edge has its own independent failure probability), providing guarantees analogous to the uniform-p model.

Background

The paper analyzes the setting where all edges fail independently with the same probability 1 - p and provides near-linear-size constructions with strong deficiency and hop guarantees.

A natural generalization is a heterogeneous model in which each pair of points has an explicitly given failure probability, requiring new techniques to balance reliability across the graph while maintaining sparsity and path-length guarantees.