What's hot and what's not: tracking most frequent items dynamically
Proceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Group Testing Problems with Sequences in Experimental Molecular Biology
SEQUENCES '97 Proceedings of the Compression and Complexity of Sequences 1997
International Journal of Bioinformatics Research and Applications
Group testing for image compression
IEEE Transactions on Image Processing
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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.