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- W302743665 abstract "Let G = (V, E) be an undirected tree representing a system in such a way that each edge corresponds to a system component. Each edge (i.e., component) may become faulty. Assuming that at most one edge becomes faulty at any time, we want to detect and locate a faulty edge if one exists, by applying tests to G. A test performed between a pair of vertices u and v can detect the existence of a faulty edge on the path between u and v (but cannot locate it if the path has more than one edge). Let VL and VM denote the set of vertices with degree one and the set of vertices with degree two in G, respectively. Our main result shows that a minimal test set (i.e., a test set detecting and locating a faulty edge with the minimum number of tests) has [1/2|VL|+1/2|VM|] tests if |VM|⩾|VL| and [2/3|VL|+1/3|VM|] tests if |VM| ≤ |VL|, expect for one special tree with seven vertices, where |·| denotes the cardinality of the set therein and [·] denotes the smallest integer not smaller than the number therein. Moreover, such a minimal test set can be constructed in O(|V|2) time." @default.
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- W302743665 date "1981-01-01" @default.
- W302743665 modified "2023-10-16" @default.
- W302743665 title "Minimal Test Set for Diagnosing a Tree System" @default.
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- W302743665 doi "https://doi.org/10.1016/s0304-0208(08)73468-6" @default.
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