Best Paper Award

An Approximate Maximum Clique Algorithm Using Integer Programming for Uniform Test Assembly

Takatoshi ISHII, Takako AKAKURA, Maomi UENO

[Trans. Inf. & Syst. (JPN Edition) , Vol.J100-D, No.1 January 2017]

  E-testing is a technology to measure the examineesf ability by testing with ICT and has recently been applied to various entrance and qualification exams. Such exams are required to estimate the examineesf ability appropriately without the same questions in taking the exams multiple times. It is one of the essential topics in this research area to generate a large number of uniform tests from a large-scale test item database since each uniform test should have the same statistical characteristics even if test items are entirely different.
  The authors formulated this problem as a maximum clique problem, which was an optimization problem defined on the graph, to search for combinations of problems with desired properties from the database in their previous research. However, it was not possible to assemble a sufficient quantity of tests in a real time and environment. In this paper, they propose an approximate algorithm that reduces the amount of computational space required for calculation by constructing only the vertices connected to the exploring clique using integer programming. Furthermore, they discuss under what conditions the proposed algorithm shows good performance based on experiments using simulations and actual data. The results indicate that the proposed method has an advantage in the case of large-scale problem databases.
  From the above considerations, the automatic generation of the uniform test assembly for large-scale problem databases is an important task in e-testing and the proposed method, which can generate more tests than the previous method, contributes to the development of this research field. This paper is consequently appreciated for a Best Paper Award.
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