Exact Learning of Weighted Graphs Using Composite Queries
This addresses a graph reconstruction problem for theoretical computer science, but it appears incremental as it builds on known query-based methods.
The paper tackles the problem of exactly reconstructing weighted graphs using composite queries, showing that simple shortest-path queries are insufficient and achieving reconstruction with a subquadratic number of queries.
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.