Exact Learning of Weighted Graphs Using Composite Queries

TL;DR

This paper investigates the problem of exactly reconstructing weighted graphs through composite queries, proposing methods to efficiently learn all edges and weights with fewer queries than quadratic in the number of vertices.

Contribution

It introduces novel composite query strategies that enable exact weighted graph reconstruction with subquadratic query complexity.

Findings

Composite queries reduce the number of queries needed for graph reconstruction.

Simple shortest-path queries are insufficient for weighted graph learning.

Proposed methods achieve efficient exact learning of weighted graphs.

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.