VNOI Problem Set Coverage Audit Against Spine-Cluster Variation Axes

The Spine-Cluster architecture for Vietnamese competitive-programming pedagogy [1] separates the cognitiveprogression axis (a linear spine of seven recognition-anddeployment milestones) from algorithmic content (nine star clusters, one per algorithm family, each defined by three or more variation axes drawn from the deep-structural dimensions experts use to classify problems). The architecture is contentagnostic and presupposes that a problem set exists which densely covers the variation axes of each cluster. The Vietnamese specialised-informatics tradition has, since 2014, increasingly directed its students toward the Vietnam Olympiad in Informatics (VNOI) online judge as the canonical problem archive; the SpineCluster framework can be operationalised against the VNOI archive only if VNOI's problems span the variation axes densely enough to support cluster-level interleaved-variation training. This paper conducts a paper-grade coverage audit of the VNOI archive against the Spine-Cluster variation-axis framework. The audit is a document-analysis synthesis, not a live archive scrape: it draws on the publicly-documented VNOI structure (the VNOI Wiki algorithm catalogue, the VNOI Online Judge problem index, the Vietnamese specialised-informatics canonical textbooks, and the practitioner-pedagogy reference textbooks of Halim, Laaksonen, Skiena, and the IOI Syllabus). Nine algorithm families are enumerated, three to five Spine-Cluster variation axes are listed per family, and a four-level coverage score (high, medium, low, gap) is assigned to each family-axis pair using a documented scoring rule. The audit identifies fifteen specific gaps where supplementary problem-set authoring is recommended; the most consequential are dynamic-programming-ontrees, parametric and "binary-search-on-the-answer" patterns, heavy-light decomposition and centroid-decomposition on trees, matroid-style greedy, and suffix-structure-based string problems. The audit is structured-judgement, not empirical enumeration; the auditing rule for each cell of the coverage matrix is stated so that the audit can be lifted to direct enumeration once judgelevel archive analysis becomes scope. The audit-loop integration specification ties the gap list into the Spine-Cluster validation pipeline and into the CPP Vol 6 and Vol 7 second-edition authoring backlog.