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@PHDTHESIS{Allemann:59084,
      author       = {Allemann, Andreas},
      othercontributors = {Triesch, Eberhard},
      title        = {{I}mproved upper bounds for several variants of group
                      testing},
      address      = {Aachen},
      publisher    = {Publikationsserver der RWTH Aachen University},
      reportid     = {RWTH-CONV-120900},
      pages        = {IV, 48 S. : graph. Darst.},
      year         = {2003},
      note         = {Aachen, Techn. Hochsch., Diss., 2003},
      abstract     = {Group testing is a class of search problems, in which we
                      aim to identify all of n items as either good or defective.
                      We may perform tests on arbitrary subsets, which indicate
                      whether the tested group contains only good items or at
                      least one defective. In the (d,n) and generalized (d,n)
                      group testing problems, it is known that the number of
                      defectives is exactly d respectively at most d and we try to
                      minimize the worst case number of tests. In this thesis, we
                      introduce a generalization of these problems by requiring
                      the case of more than d defectives to be detected as well
                      and prove that solving the new problem needs exactly one
                      more test than the (d,n) group testing problem. The major
                      result is a new algorithm for all these problems whose
                      required number of tests is for n/d >= 2 less than 0.255d +
                      0.5log2 d + 5.5 above the information lower bound. For d >=
                      10, this is below the best known upper bound of d - 1
                      additional tests given in the literature.},
      keywords     = {Gruppentesten (SWD)},
      cin          = {100000},
      ddc          = {510},
      cid          = {$I:(DE-82)100000_20140620$},
      typ          = {PUB:(DE-HGF)11},
      urn          = {urn:nbn:de:hbz:82-opus-7049},
      doi          = {10.18154/RWTH-CONV-120900},
      url          = {https://publications.rwth-aachen.de/record/59084},
}