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Liaoning Normal University

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Representative Papers

Stochasticity Is Not the Hard Part: Reduction and Complexity in Instructional Sequencing over Prerequisite DAGs

Aug 05, 2026

This study addresses the problem of finding the optimal teaching sequence that minimizes learning cost in scenarios with prerequisite dependencies. The problem is modeled as a stochastic shortest path problem, and we propose an exact reduction based on lattice theory that transforms it into a deterministic shortest path problem, revealing that the computational difficulty stems not from stochasticity but from the combinatorial complexity inherent in the dependency structure. We theoretically prove the problem to be NP-hard; however, by leveraging dynamic programming, A* search, and feedback arc set reductions, we identify a “doubly simple” regime in real-world course data where A* efficiently solves instances with state-space size linear in the number of concepts. A computable diagnostic metric, \( m\Delta \), further enables practical assessment of instance hardness.

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Latest Papers

Stochasticity Is Not the Hard Part: Reduction and Complexity in Instructional Sequencing over Prerequisite DAGs

Aug 05, 2026

This study addresses the problem of finding the optimal teaching sequence that minimizes learning cost in scenarios with prerequisite dependencies. The problem is modeled as a stochastic shortest path problem, and we propose an exact reduction based on lattice theory that transforms it into a deterministic shortest path problem, revealing that the computational difficulty stems not from stochasticity but from the combinatorial complexity inherent in the dependency structure. We theoretically prove the problem to be NP-hard; however, by leveraging dynamic programming, A* search, and feedback arc set reductions, we identify a “doubly simple” regime in real-world course data where A* efficiently solves instances with state-space size linear in the number of concepts. A computable diagnostic metric, \( m\Delta \), further enables practical assessment of instance hardness.

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