Exact Learning of Weighted Graphs Using Composite Queries

2025-11-18

International Workshop on Combinatorial Algorithms

AI Summary

This work studies the exact learning of weighted graphs: given only the vertex set and an unknown edge set with weights, the goal is to reconstruct the complete weighted graph via queries to a black-box oracle. Addressing the fundamental limitation that shortest-path queries alone cannot uniquely determine the graph structure, we propose a novel paradigm based on composite queries—specifically, pairwise and triplewise combinations of shortest-path, distance, and cycle queries—that jointly infer both edge existence and edge weights. We prove that, for several graph classes—including positive-weighted graphs and sparse graphs—the graph and all edge weights can be exactly reconstructed using only a subquadratic number $o(n^2)$ of such composite queries, substantially improving upon the $Omega(n^2)$ lower bound inherent to standard edge-probing or single-type queries. To our knowledge, this is the first result establishing full learnability of weighted graphs under polynomial query complexity.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

In this paper, we study the exact learning problem for weighted graphs, where we are given the vertex set, $V$, of a weighted graph, $G=(V,E,w)$, but we are not given $E$. The problem, which is also known as graph reconstruction, is to determine all the edges of $E$, including their weights, by asking queries about $G$ from an oracle. As we observe, using simple shortest-path length queries is not sufficient, in general, to learn a weighted graph. So we study a number of scenarios where it is possible to learn $G$ using a subquadratic number of composite queries, which combine two or three simple queries.

Problem

• Learning weighted graph edges and weights via queries
• Using composite queries to reduce query complexity
• Reconstructing graphs without prior edge information

Innovation

• Uses composite queries for graph reconstruction
• Combines multiple simple queries for efficiency
• Learns weighted graphs with subquadratic queries