An Approximation Algorithm for Graph Label Selection

TL;DR

This paper introduces the first provable approximation algorithm for the graph label selection problem, balancing theoretical guarantees with practical scalability.

Contribution

It presents a novel $ ilde{O}( ext{log}^{1.5} n)$-approximation algorithm with provable guarantees, improving over heuristics and resource-augmented methods.

Findings

First $ ilde{O}( ext{log}^{1.5} n)$-approximation algorithm for graph label selection.

Practical heuristics derived from the algorithm scale to larger graphs.

Heuristics retain quality comparable to the theoretical algorithm.

Abstract

In the graph label selection problem, one is given an $n$-vertex graph and a budget $k$, and seeks to select $k$ vertices whose labels enable accurate prediction of the labels on the remaining vertices. This problem formalizes distilling a small representative set from the whole graph. We present the first $\tilde{O}(\log^{1.5} n)$-approximation algorithm for graph label selection under the standard budget constraint. Prior work either relies on resource augmentation, allowing substantially more than $k$ labeled vertices, or consists primarily of heuristics without provable guarantees. Finally, we demonstrate that practical heuristic variants of our algorithm scale to significantly larger graphs than previous methods, while essentially retaining their quality.