Combinatorial group testing methods for the BIST diagnosis problem
Proceedings of the 2004 Asia and South Pacific Design Automation Conference
Improved Results for Competitive Group Testing
Combinatorics, Probability and Computing
Searching for two counterfeit coins with two-arms balance
Discrete Applied Mathematics
An improved model-based method to test circuit faults
Theoretical Computer Science
Embedded fault diagnosis in digital systems with BIST
Microprocessors & Microsystems
Experimental comparison of different diagnosis algorithms in the BIST environment
ASM '07 The 16th IASTED International Conference on Applied Simulation and Modelling
Searching for two counterfeit coins with two-arms balance
Discrete Applied Mathematics
Competitive group testing and learning hidden vertex covers with minimum adaptivity
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
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Many fault-detection problems fall into the following model: There is a set of $n$ items, some of which are defective. The goal is to identify the defective items by using the minimum number of tests. Each test is on a subset of items and tells whether the subset contains a defective item or not. Let $M_{\alpha}(d, n) (M_{\alpha}(d\,|\,n))$ denote the maximum number of tests for an algorithm $\alpha$ to identify $d$ defectives from a set of $n$ items provided that $d$, the number of defective items, is known (unknown) before the testing. Let $M(d, n) = \min_{\alpha} M_{\alpha}(d, n)$. An algorithm $\alpha$ is called a {\it competitive algorithm\/} if there exist constants $c$ and $a$ such that for all $n d 0$, $M_{\alpha}(d\,|\,n) \leq cM(d, n) + a$. This paper confirms a recent conjecture that there exists a bisecting algorithm $A$ such that $M_A(d\,|\,n) \leq 2M(d, n) + 1$. Also, an algorithm $B$ such that $M_B(d\,|\,n) \leq 1.65M(d, n) + 10$ is presented.