Adaptive Vantage Point Selection Bounds

Determine whether the lower bounds proved for non-adaptive vantage point selection extend to the adaptive setting, or whether an adaptive algorithm can achieve a competitive ratio better than the non-adaptive lower bound.

Background

The paper establishes tight, up to polylogarithmic factors, expected competitive-ratio bounds for randomized non-adaptive algorithms solving the vantage point selection problem on weighted graphs with unique shortest paths. In this model, an algorithm selects all of its vantage points before observing any capacity information or revealed bottleneck edges, while the benchmark optimum knows the edge capacities in advance.

The lower-bound construction is specifically designed for the non-adaptive setting: the authors note that an adaptive algorithm might use information obtained from an initial query to locate the hidden optimal vantage point within a butterfly component. The paper therefore leaves unresolved whether comparable lower bounds hold when future queries may depend on previously revealed bottleneck edges, or whether adaptivity permits an algorithm to outperform the established non-adaptive lower bound.