Dagstuhl Seminar Proceedings, Volume 9281

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09281 Abstracts Collection – Search Methodologies

Authors: Rudolf Ahlswede, Ferdinando Cicalese, and Ugo Vaccaro

Abstract

From 05.07.09 to 10.07.09, the Dagstuhl Seminar 09281 on ``Search Methodologies '' was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. Abstracts of the presentations given during the seminar are put together in this paper. The first section describes the seminar topics and goals in general. We also briefly comment on how the topics were addressed in the talks. Links to extended abstracts or full papers are provided, if available.

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Rudolf Ahlswede, Ferdinando Cicalese, and Ugo Vaccaro. 09281 Abstracts Collection – Search Methodologies. In Search Methodologies. Dagstuhl Seminar Proceedings, Volume 9281, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{ahlswede_et_al:DagSemProc.09281.1,
  author =	{Ahlswede, Rudolf and Cicalese, Ferdinando and Vaccaro, Ugo},
  title =	{{09281 Abstracts Collection – Search Methodologies}},
  booktitle =	{Search Methodologies},
  pages =	{1--15},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9281},
  editor =	{Rudolf Ahlswede and Ferdinando Cicalese and Ugo Vaccaro},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09281.1},
  URN =		{urn:nbn:de:0030-drops-22457},
  doi =		{10.4230/DagSemProc.09281.1},
  annote =	{Keywords: Search algorithms, group testing, fault-tolerance, identification, decision tree, multi-access communication}
}

Document

DOI: 10.4230/DagSemProc.09281.2

Explicit Non-Adaptive Combinatorial Group Testing Schemes

Authors: Ely Porat and Amir Rotschild

Abstract

Group testing is a long studied problem in combinatorics: A small set of r ill people should be identified out of the whole (n people) by using only queries (tests) of the form "Does set X contain an ill human?". In this paper we provide an explicit construction of a testing scheme which is better (smaller) than any known explicit construction. This scheme has \Theta(min[r2 log n, n])tests which is as many as the best non-explicit schemes have. In our construction we use a fact that may have a value by its own right: Linear error-correction codes with parameters [m, k, \delta m]q meeting the Gilbert-Varshamov bound may be constructed quite efficiently, in \Theta[q^{k}m) time.

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Ely Porat and Amir Rotschild. Explicit Non-Adaptive Combinatorial Group Testing Schemes. In Search Methodologies. Dagstuhl Seminar Proceedings, Volume 9281, pp. 1-13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{porat_et_al:DagSemProc.09281.2,
  author =	{Porat, Ely and Rotschild, Amir},
  title =	{{Explicit Non-Adaptive Combinatorial Group Testing Schemes}},
  booktitle =	{Search Methodologies},
  pages =	{1--13},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9281},
  editor =	{Rudolf Ahlswede and Ferdinando Cicalese and Ugo Vaccaro},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09281.2},
  URN =		{urn:nbn:de:0030-drops-22414},
  doi =		{10.4230/DagSemProc.09281.2},
  annote =	{Keywords: Prime Numbers, Group Testing, Streaming, Pattern Matching}
}

Document

DOI: 10.4230/DagSemProc.09281.3

Locating and Detecting Arrays for Interaction Faults

Authors: Charles J. Colbourn and Daniel W. McClary

Abstract

The identification of interaction faults in component-based systems has focused on indicating the presence of faults, rather than their location and magnitude. While this is a valuable step in screening a system for interaction faults prior to its release, it provides little information to assist in the correction of such faults. Consequently tests to reveal the location of interaction faults are of interest. The problem of nonadaptive location of interaction faults is formalized under the hypothesis that the system contains (at most) some number d of faults, each involving (at most) some number t of interacting factors. Restrictions on the number and size of the putative faults lead to numerous variants of the basic problem. The relationships between this class of problems and interaction testing using covering arrays to indicate the presence of faults, designed experiments to measure and model faults, and combinatorial group testing to locate faults in a more general testing scenario, are all examined. While each has some definite similarities with the fault location problems for component-based systems, each has some striking differences as well. In this paper, we formulate the combinatorial problems for locating and detecting arrays to undertake interaction fault location. Necessary conditions for existence are established, and using a close connection to covering arrays, asymptotic bounds on the size of minimal locating and detecting arrays are established. A final version of this paper appears in J Comb Optim (2008) 15: 17-48.

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Charles J. Colbourn and Daniel W. McClary. Locating and Detecting Arrays for Interaction Faults. In Search Methodologies. Dagstuhl Seminar Proceedings, Volume 9281, pp. 1-34, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{colbourn_et_al:DagSemProc.09281.3,
  author =	{Colbourn, Charles J. and McClary, Daniel W.},
  title =	{{Locating and Detecting Arrays for Interaction Faults}},
  booktitle =	{Search Methodologies},
  pages =	{1--34},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9281},
  editor =	{Rudolf Ahlswede and Ferdinando Cicalese and Ugo Vaccaro},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09281.3},
  URN =		{urn:nbn:de:0030-drops-22405},
  doi =		{10.4230/DagSemProc.09281.3},
  annote =	{Keywords: Covering array, Orthogonal array, Factorial design, Cover-free family, Disjunct matrix, Locating array, Detecting array}
}

Document

DOI: 10.4230/DagSemProc.09281.4

Minimax Trees in Linear Time with Applications

Authors: Pawel Gawrychowski and Travis Gagie

Abstract

A minimax tree is similar to a Huffman tree except that, instead of minimizing the weighted average of the leaves' depths, it minimizes the maximum of any leaf's weight plus its depth. Golumbic (1976) introduced minimax trees and gave a Huffman-like, $O (n log n)$-time algorithm for building them. Drmota and Szpankowski (2002) gave another $O (n log n)$-time algorithm, which takes linear time when the weights are already sorted by their fractional parts. In this paper we give the first linear-time algorithm for building minimax trees for unsorted real weights.

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Pawel Gawrychowski and Travis Gagie. Minimax Trees in Linear Time with Applications. In Search Methodologies. Dagstuhl Seminar Proceedings, Volume 9281, pp. 1-11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{gawrychowski_et_al:DagSemProc.09281.4,
  author =	{Gawrychowski, Pawel and Gagie, Travis},
  title =	{{Minimax Trees in Linear Time with Applications}},
  booktitle =	{Search Methodologies},
  pages =	{1--11},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9281},
  editor =	{Rudolf Ahlswede and Ferdinando Cicalese and Ugo Vaccaro},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09281.4},
  URN =		{urn:nbn:de:0030-drops-22421},
  doi =		{10.4230/DagSemProc.09281.4},
  annote =	{Keywords: Data structures, data compression, prefix-free coding}
}

Document

DOI: 10.4230/DagSemProc.09281.5

Pattern matching with don't cares and few errors

Authors: Raphael Clifford, Klim Efremo, Ely Porat, and Amir Rotschild

Abstract

We present solutions for the k-mismatch pattern matching problem with don't cares. Given a text t of length n and a pattern p of length m with don't care symbols and a bound k, our algorithms find all the places that the pattern matches the text with at most k mismatches. We first give an \Theta(n(k + logmlog k) log n) time randomised algorithm which finds the correct answer with high probability. We then present a new deter- ministic \Theta(nk^2 log^m)time solution that uses tools originally developed for group testing. Taking our derandomisation approach further we de- velop an approach based on k-selectors that runs in \Theta(nk polylogm) time. Further, in each case the location of the mismatches at each alignment is also given at no extra cost.

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Raphael Clifford, Klim Efremo, Ely Porat, and Amir Rotschild. Pattern matching with don't cares and few errors. In Search Methodologies. Dagstuhl Seminar Proceedings, Volume 9281, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{clifford_et_al:DagSemProc.09281.5,
  author =	{Clifford, Raphael and Efremo, Klim and Porat, Ely and Rotschild, Amir},
  title =	{{Pattern matching with don't cares and few errors}},
  booktitle =	{Search Methodologies},
  pages =	{1--19},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9281},
  editor =	{Rudolf Ahlswede and Ferdinando Cicalese and Ugo Vaccaro},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09281.5},
  URN =		{urn:nbn:de:0030-drops-22442},
  doi =		{10.4230/DagSemProc.09281.5},
  annote =	{Keywords: Prime Numbers, Group Testing, Streaming, Pattern Matching}
}

Document

DOI: 10.4230/DagSemProc.09281.6

Rounds in Combinatorial Search

Authors: Gábor Wiener

Abstract

The search complexity of a separating system ${cal H} subseteq 2^{[m]}$ is the minimum number of questions of type ``$xin H$? hinspace '' (where $H in {cal H}$) needed in the worst case to determine a hidden element $xin [m]$. If we are allowed to ask the questions in at most $k$ batches then we speak of the emph{$k$-round} (or emph{$k$-stage}) complexity of ${cal H}$, denoted by $hbox{c}_k ({cal H})$. While $1$-round and $m$-round complexities (called non-adaptive and adaptive complexities, respectively) are widely studied (see for example Aigner cite{A}), much less is known about other possible values of $k$, though the cases with small values of $k$ (tipically $k=2$) attracted significant attention recently, due to their applications in DNA library screening. It is clear that $ |{cal H}| geq hbox{c}_{1} ({cal H}) geq hbox{c}_{2} ({cal H}) geq ldots geq hbox{c}_{m} ({cal H})$. A group of problems raised by {G. O. H. Katona} cite{Ka} is to characterize those separating systems for which some of these inequalities are tight. In this paper we are discussing set systems ${cal H}$ with the property $|{cal H}| = hbox{c}_{k} ({cal H}) $ for any $kgeq 3$. We give a necessary condition for this property by proving a theorem about traces of hypergraphs which also has its own interest.

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Gábor Wiener. Rounds in Combinatorial Search. In Search Methodologies. Dagstuhl Seminar Proceedings, Volume 9281, pp. 1-5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{wiener:DagSemProc.09281.6,
  author =	{Wiener, G\'{a}bor},
  title =	{{Rounds in Combinatorial Search}},
  booktitle =	{Search Methodologies},
  pages =	{1--5},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9281},
  editor =	{Rudolf Ahlswede and Ferdinando Cicalese and Ugo Vaccaro},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09281.6},
  URN =		{urn:nbn:de:0030-drops-22399},
  doi =		{10.4230/DagSemProc.09281.6},
  annote =	{Keywords: Search, group testing, adaptiveness, hypergraph, trace}
}

Document

DOI: 10.4230/DagSemProc.09281.7

Some Aspects of Finite State Channel related to Hidden Markov Process

Authors: Kingo Kobayashi

Abstract

We have no satisfactory capacity formula for most channels with finite states. Here, we consider some interesting examples of finite state channels, such as Gilbert-Elliot channel, trapdoor channel, etc., to reveal special characters of problems and difficulties to determine the capacities. Meanwhile, we give a simple expression of the capacity formula for Gilbert-Elliot channel by using a hidden Markov source for the optimal input process. This idea should be extended to other finite state channels.

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Kingo Kobayashi. Some Aspects of Finite State Channel related to Hidden Markov Process. In Search Methodologies. Dagstuhl Seminar Proceedings, Volume 9281, pp. 1-16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{kobayashi:DagSemProc.09281.7,
  author =	{Kobayashi, Kingo},
  title =	{{Some Aspects of Finite State Channel related to Hidden Markov Process}},
  booktitle =	{Search Methodologies},
  pages =	{1--16},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9281},
  editor =	{Rudolf Ahlswede and Ferdinando Cicalese and Ugo Vaccaro},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09281.7},
  URN =		{urn:nbn:de:0030-drops-22434},
  doi =		{10.4230/DagSemProc.09281.7},
  annote =	{Keywords: Finite state channel, Hidden Markov source, Gilbert-Elliot channel, Trapdoor Channel}
}

Dagstuhl Seminar Proceedings, Volume 9281

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09281 Abstracts Collection – Search Methodologies

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Explicit Non-Adaptive Combinatorial Group Testing Schemes

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Locating and Detecting Arrays for Interaction Faults

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Minimax Trees in Linear Time with Applications

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Pattern matching with don't cares and few errors

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Rounds in Combinatorial Search

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Some Aspects of Finite State Channel related to Hidden Markov Process

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