[{"abstract":[{"text":"Already in his Lectures on Search [A. Rdnyi, Lectures on the theory of search, University of North Carolina, Chapel Hill, Institute of Statistics, Mimeo Series No. 6007, 1969. [11]] Renyi suggested to consider a search problem, where an unknown x is an element of X = {1, 2, ..., n} is to be found by asking for containment in a minimal number m(n, k) of subsets A(1),...,A(m) with the restrictions vertical bar A(i)vertical bar <= k < n/2 for i = 1, 2,..., m. Katona gave in 1966 the lower bound m(n, k) >= log n/h (k/n) in terms of binary entropy and the upper bound m(n, k) <= inverted right perpendicular log n + 1) / log n/k inverted left perpendicular which was improved by Wegener in 1979 to m(n, k) <= inverted right perpendicular log n / log n/k inverted left perpendicular (inverted right perpendicular n/k inverted left perpendicular - 1). We prove here for k=pn that m (n, k)=log n+o(log n)/h (p), that is, ratewise optimality of the entropy bound: lim(n ->infinity) m (n, pn)/logn = 1/h(p). Actually this work was motivated by a more recent study of Karpovsky, Chakrabarty, Levitin and Avresky of a problem on fault diagnosis in hypercubes, which amounts to finding the minimal number M(n, r) of Hamming balls of radius r = rho n with rho <= 1/2 in the Hamming space H-n = {0, 1}(n), which separate the vertices. Their bounds on M(n, r) are far from being optimal. We establish bounds implying lim(n ->infinity) 1/n log M(n, r) = 1 - h(rho). However, it must be emphasized that the methods of prove for our two upper bounds are quite different. (C) 2007 Elsevier B.V. All rights reserved.","lang":"eng"}],"author":[{"last_name":"Ahlswede","first_name":"Rudolf","full_name":"Ahlswede, Rudolf","id":"10479"}],"publisher":"Elsevier","quality_controlled":"1","status":"public","intvolume":" 156","date_updated":"2018-07-24T12:58:38Z","department":[{"_id":"10020"}],"citation":{"mla":"Ahlswede, Rudolf. “Ratewise-optimal non-sequential search strategies under constraints on the tests”. *Discrete Applied Mathematics* 156.9: Special Issue (2008): 1431-1443.","harvard1":"Ahlswede, R., 2008. Ratewise-optimal non-sequential search strategies under constraints on the tests. *Discrete Applied Mathematics*, 156(9: Special Issue), p 1431-1443.","ama":"Ahlswede R. Ratewise-optimal non-sequential search strategies under constraints on the tests. *Discrete Applied Mathematics*. 2008;156(9: Special Issue):1431-1443.","dgps":"Ahlswede, R. (2008). Ratewise-optimal non-sequential search strategies under constraints on the tests. *Discrete Applied Mathematics*, *156*(9: Special Issue), 1431-1443. Elsevier. doi:10.1016/j.dam.2006.06.013.

","aps":" R. Ahlswede, Ratewise-optimal non-sequential search strategies under constraints on the tests, Discrete Applied Mathematics **156**, 1431 (2008).","ieee":" R. Ahlswede, “Ratewise-optimal non-sequential search strategies under constraints on the tests”, *Discrete Applied Mathematics*, vol. 156, 2008, pp. 1431-1443.","bio1":"Ahlswede R (2008)

Ratewise-optimal non-sequential search strategies under constraints on the tests.

Discrete Applied Mathematics 156(9: Special Issue): 1431-1443.","wels":"Ahlswede, R. (2008): Ratewise-optimal non-sequential search strategies under constraints on the tests *Discrete Applied Mathematics*,156:(9: Special Issue): 1431-1443.","angewandte-chemie":"R. Ahlswede, “Ratewise-optimal non-sequential search strategies under constraints on the tests”, *Discrete Applied Mathematics*, **2008**, *156*, 1431-1443.","apa_indent":"Ahlswede, R. (2008). Ratewise-optimal non-sequential search strategies under constraints on the tests. *Discrete Applied Mathematics*, *156*(9: Special Issue), 1431-1443. doi:10.1016/j.dam.2006.06.013

","apa":"Ahlswede, R. (2008). Ratewise-optimal non-sequential search strategies under constraints on the tests. *Discrete Applied Mathematics*, *156*(9: Special Issue), 1431-1443. doi:10.1016/j.dam.2006.06.013","chicago":"Ahlswede, Rudolf. 2008. “Ratewise-optimal non-sequential search strategies under constraints on the tests”. *Discrete Applied Mathematics* 156 (9: Special Issue): 1431-1443.

","lncs":" Ahlswede, R.: Ratewise-optimal non-sequential search strategies under constraints on the tests. Discrete Applied Mathematics. 156, 1431-1443 (2008).","frontiers":"Ahlswede, R. (2008). Ratewise-optimal non-sequential search strategies under constraints on the tests. *Discrete Applied Mathematics* 156, 1431-1443.","default":"Ahlswede R (2008)

*Discrete Applied Mathematics* 156(9: Special Issue): 1431-1443."},"publication_status":"published","external_id":{"isi":["000255804200007"]},"year":"2008","keyword":["search strategies"],"publication_identifier":{"issn":["0166-218X"]},"volume":"156","doi":"10.1016/j.dam.2006.06.013","type":"journal_article","date_created":"2010-04-26T09:44:15Z","isi":1,"page":"1431-1443","first_author":"Ahlswede, Rudolf","_id":"1587890","language":[{"iso":"eng"}],"title":"Ratewise-optimal non-sequential search strategies under constraints on the tests","publication":"Discrete Applied Mathematics","edit_mode":"expert","issue":"9: Special Issue"}]