1Cademy - Deterministic BFS Upward/Downward Traversal from Dense Seeds in Bidirectional Diffusion

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Dense-Seeded Local Diffusion with Additive Hop Penalty and Max Aggregation
Breadth-First Search (BFS) on Graphs
Bidirectional Diffusion (Method) in Auditable Strict-Parity Evaluation of Prerequisite-Graph Retrieval for RAG under Leakage Controls

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Deterministic BFS Upward/Downward Traversal from Dense Seeds in Bidirectional Diffusion

From the dense seeds, the bidirectional-diffusion retriever runs deterministic breadth-first traversals in the prerequisite DAG, one upward toward ancestors and one downward toward descendants, each truncated at the per-query depths $d_\uparrow$ and $d_\downarrow$ chosen by the adaptive controller. Because the traversals are deterministic BFS rather than a stochastic random walk, the truncated ancestor and descendant path sets $\mathcal{P}_\uparrow(v)$ and $\mathcal{P}_\downarrow(v)$ that feed the path-score formulas are reproducible given the graph, the seeds, and the chosen depths.

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Updated 2026-05-18

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Reference: Auditable Strict-Parity Evaluation of Prerequisite-Graph Retrieval for RAG under Leakage Controls

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