Searching for faulty leaves in binary trees
Let us be given a complete binary tree where an unknown subset of the leaves is faulty. Suppose that we can test any node whether there is a faulty leaf in the subtree routed at that node. Our aim is to give a strategy for finding all faults that minimizes the worst-case search length for a previously estimated number of faults. This question is of immediate interest in VLSI circuit checking. In this paper we give an elementary proof of the optimality of a very simple test strategy.
KeywordsSearch Process Binary Tree Complete Binary Tree Maximal Antichain Faulty Cell
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- M.Aigner: Combinatorial Search, Wiley-Teubner 1988Google Scholar
- I.Althöfer, E.Triesch: Edge search in graphs and hypergraphs of bounded rank, Discrete Math. 115 (1993), 1–9Google Scholar
- G.J.Chang, F.K.Hwang, S.Lin: Group testing with two defectives, Discrete Applied Math. 4 (1982), 97–102Google Scholar
- P.Damašchke: A tight upper bound for group testing in graphs, Discrete Applied Math. 48 (1994), 101–109Google Scholar
- P.Damaschke: A parallel algorithm for nearly optimal edge search, Information Processing Letters, to appearGoogle Scholar
- C.Elm, D.Tavangarian: Fault detection and fault localization using IDDQ-testing in parallel testable FAST-SRAMs, 12th IEEE VLSI Test Symposium, Cherry Hill/NJ 1994Google Scholar
- A.J.van de Goor: Testing Semiconductor Memories, Theory and Practice, John Wiley & Sons, Chichester 1991Google Scholar
- E.Triesch: A group testing problem for hypergraphs of bounded rank, submitted to Discrete Math. Google Scholar