Uncertain graphs serve as valuable tools for representing the inherent uncertainty within complex systems. This project delves into an extensive examination and expansion of Jin et al.'s work, with a specific focus on the challenging task of identifying the k most reliable subgraphs within uncertain graphs. This problem holds great relevance across various network applications, including but not limited to social networks, network routing, and protein-protein interaction networks.

Due to its #P-completeness, rendering it computationally intractable, we introduce a novel sampling scheme aimed at providing ε-approximations with a high level of confidence. In the pursuit of this goal, we employ a transformation that reconfigures the problem into one of uncovering the k most frequent cohesive sets within deterministic graphs. This transformation paves the way for two distinct strategies: the eager approach and the attentive approach.

The eager approach seamlessly combines peeling techniques with an iterative variant of the Apriori algorithm to furnish approximate solutions, complete with ε-guarantees. In parallel, the attentive approach builds upon the foundation of the eager approach by incorporating a progressive sampling step. Together, these two methodologies offer a versatile framework that allows for a judicious trade-off between computational efficiency and result precision.

Extensive experimentation serves to validate the efficacy of these innovative approaches. Our findings conclusively demonstrate significant improvements over a straightforward extension of Jin et al.'s work to the top-k subgraph discovery problem.

To provide clarity and consistency with the report's content, we introduce the following equivalences:

TopKPeeling is synonymous with AttentivePeeling. TopKSingleStep corresponds to EagerPeeling. NaiveTopKPeeling is equivalent to NaivePeeling.