See the Tree Through the Lines: The Shazoo Algorithm -- Full Version --

TL;DR

The paper introduces Shazoo, an efficient and nearly optimal algorithm for node prediction in weighted trees, outperforming existing methods and applicable to real-world datasets.

Contribution

It presents Shazoo, a novel algorithm that generalizes previous approaches and achieves near-optimal predictions for weighted trees.

Findings

Shazoo performs close to energy minimization methods on real datasets.

It is nearly optimal for weighted trees.

Shazoo generalizes previous unweighted and line prediction algorithms.

Abstract

Predicting the nodes of a given graph is a fascinating theoretical problem with applications in several domains. Since graph sparsification via spanning trees retains enough information while making the task much easier, trees are an important special case of this problem. Although it is known how to predict the nodes of an unweighted tree in a nearly optimal way, in the weighted case a fully satisfactory algorithm is not available yet. We fill this hole and introduce an efficient node predictor, Shazoo, which is nearly optimal on any weighted tree. Moreover, we show that Shazoo can be viewed as a common nontrivial generalization of both previous approaches for unweighted trees and weighted lines. Experiments on real-world datasets confirm that Shazoo performs well in that it fully exploits the structure of the input tree, and gets very close to (and sometimes better than) less scalable energy minimization methods.