Learning Graph Partitions

by   Sayan Mukherjee, et al.

Given a partition of a graph into connected components, the membership oracle asserts whether any two vertices of the graph lie in the same component or not. We prove that for n≥ k≥ 2, learning the components of an n-vertex hidden graph with k components requires at least 1/2(n-k)(k-1) membership queries. This proves the optimality of the O(nk) algorithm proposed by Reyzin and Srivastava (2007) for this problem, improving on the best known information-theoretic bound of Ω(nlog k) queries. Further, we construct an oracle that can learn the number of components of G in asymptotically fewer queries than learning the full partition, thus answering another question posed by the same authors. Lastly, we introduce a more applicable version of this oracle, and prove asymptotically tight bounds of Θ(m) queries for both learning and verifying an m-edge hidden graph G using this oracle.


page 1

page 2

page 3

page 4


Modularity in Query-Based Concept Learning

We define and study the problem of modular concept learning, that is, le...

Optimal distance query reconstruction for graphs without long induced cycles

Let G=(V,E) be an n-vertex connected graph of maximum degree Δ. Given ac...

Convex optimization using quantum oracles

We study to what extent quantum algorithms can speed up solving convex o...

Finding a Small Number of Colourful Components

A partition (V_1,...,V_k) of the vertex set of a graph G with a (not nec...

Sublinear-Time Clustering Oracle for Signed Graphs

Social networks are often modeled using signed graphs, where vertices co...

Efficiently Processing Workflow Provenance Queries on SPARK

In this paper, we investigate how we can leverage Spark platform for eff...

Hyper-distance Oracles in Hypergraphs

We study point-to-point distance estimation in hypergraphs, where the qu...

Please sign up or login with your details

Forgot password? Click here to reset