Abstract
Given a finite ordered set of items and an unknown distinguished subset P of up to p positive elements, identify the items in P by asking the least number of queries of the type “does the subset Q intersect P?”, where Q is a subset of consecutive elements of {1, 2, ..., n}. This problem arises e.g. in computational biology, in a particular method for determining splice sites. We consider time-efficient algorithms where queries are arranged in a fixed number s of stages: in each stage, queries are performed in parallel. In a recent paper we devised query-optimal strategies in the special cases p=1 or s=2, subject to lower-order terms. Exploiting new ideas we are now able to provide a much neater argument that allows doubling the general lower bound for any p≥ 2 and s≥ 3. Moreover, we provide new strategies that match this new bound up to the constant of the main term. The new query scheme shows an effective use of overlapping queries within a stage. Remarkably, this contrasts with the known results for s ≤ 2 where optimal strategies were implemented by disjoint queries.
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Cicalese, F., Damaschke, P., Tansini, L., Werth, S. (2005). Overlaps Help: Improved Bounds for Group Testing with Interval Queries. In: Wang, L. (eds) Computing and Combinatorics. COCOON 2005. Lecture Notes in Computer Science, vol 3595. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11533719_94
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DOI: https://doi.org/10.1007/11533719_94
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28061-3
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