A Structural Approach to Assess Graph-Based Exercises

Abstract

This paper proposes a structure driven approach to assess graph-based exercises. Given two graphs, a solution and an attempt of a student, this approach computes a mapping between the node sets of both graphs that maximizes the student's grade, as well as a description of the differences between the two graph. The proposed algorithm uses heuristics to test the most promising mappings first and prune the remaining when it is sure that a better mapping cannot be computed. The proposed algorithm is applicable to any type of document that can be parsed into its graph-inspired data model. This data model is able to accommodate diagram languages, such as UML or ER diagrams, for which this kind of assessment is typically used. However, the motivation for developing this algorithm is to combine it with other assessment models, such as the test case model used for programming language assessment. The proposed algorithm was validated with thousands of graphs with different features produced by a synthetic data generator. Several experiments were designed to analyse the impact of different features such as graph size, and amount of difference between solution and attempt.