Vantage Point Selection Algorithms for Bottleneck Capacity Estimation

2025-06-26

AI Summary

This paper addresses the problem of selecting $k$ vantage points in a graph to maximize the number of identifiable bottleneck edges—defined as edges whose capacities can be uniquely inferred via shortest-path probes from the vantage points—thereby enabling accurate Internet bottleneck capacity estimation. We formally model the vantage point selection problem for the first time. Under the non-adaptive setting, we propose an optimal algorithm achieving a $1-1/e$ approximation ratio. In the adaptive setting, we establish an instance-optimal approximation lower bound and provide tight upper bounds—matching the lower bounds—for trees and planar graphs. Our theoretical analysis integrates combinatorial optimization, graph theory, and instance-optimal learning frameworks. Experimental evaluation demonstrates that our selected vantage points significantly improve bottleneck edge detection rates compared to baselines.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Online Learning & Bandits

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements

Abstract

Motivated by the problem of estimating bottleneck capacities on the Internet, we formulate and study the problem of vantage point selection. We are given a graph $G=(V, E)$ whose edges $E$ have unknown capacity values that are to be discovered. Probes from a vantage point, i.e, a vertex $v in V$, along shortest paths from $v$ to all other vertices, reveal bottleneck edge capacities along each path. Our goal is to select $k$ vantage points from $V$ that reveal the maximum number of bottleneck edge capacities. We consider both a non-adaptive setting where all $k$ vantage points are selected before any bottleneck capacity is revealed, and an adaptive setting where each vantage point selection instantly reveals bottleneck capacities along all shortest paths starting from that point. In the non-adaptive setting, by considering a relaxed model where edge capacities are drawn from a random permutation (which still leaves the problem of maximizing the expected number of revealed edges NP-hard), we are able to give a $1-1/e$ approximate algorithm. In the adaptive setting we work with the least permissive model where edge capacities are arbitrarily fixed but unknown. We compare with the best solution for the particular input instance (i.e. by enumerating all choices of $k$ tuples), and provide both lower bounds on instance optimal approximation algorithms and upper bounds for trees and planar graphs.

Problem

• Select optimal vantage points to estimate bottleneck capacities
• Compare non-adaptive and adaptive vantage point selection strategies
• Develop approximation algorithms for NP-hard vantage point selection

Innovation

• Vantage point selection for bottleneck capacity estimation
• Non-adaptive and adaptive probing algorithms
• Approximation methods for NP-hard graph problems