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The near-optimal test-point set selection for an analog fault dictionary is formulated as a heuristic depth-first graph search problem. Then, the test point selection process becomes a graph-node-expanding process. During the process of graph expansion, the information-theoretic concepts of entropy are used to develop the criterion for how to choose an intermediate node to expand. If a graph node has already isolated those faults that are hard isolate, then the residual faults can easily be isolated. The difficulty of isolating a given fault is evaluated by the information-theoretic concept of entropy. The harder that a fault is isolated, the larger the entropy value it will have. Statistical experimental results indicate that the proposed method more accurately finds the global minimum set of test points than other methods; therefore, it is a good solution to minimize the size of the test point set.