eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2009-11-10
9281
1
15
10.4230/DagSemProc.09281.1
article
09281 Abstracts Collection – Search Methodologies
Ahlswede, Rudolf
Cicalese, Ferdinando
Vaccaro, Ugo
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09281/DagSemProc.09281.1/DagSemProc.09281.1.pdf
Search algorithms
group testing
fault-tolerance
identification
decision tree
multi-access communication
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2009-11-10
9281
1
13
10.4230/DagSemProc.09281.2
article
Explicit Non-Adaptive Combinatorial Group Testing Schemes
Porat, Ely
Rotschild, Amir
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09281/DagSemProc.09281.2/DagSemProc.09281.2.pdf
Prime Numbers
Group Testing
Streaming
Pattern Matching
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2009-11-10
9281
1
34
10.4230/DagSemProc.09281.3
article
Locating and Detecting Arrays for Interaction Faults
Colbourn, Charles J.
McClary, Daniel W.
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09281/DagSemProc.09281.3/DagSemProc.09281.3.pdf
Covering array
Orthogonal array
Factorial design
Cover-free family
Disjunct matrix
Locating array
Detecting array
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2009-11-10
9281
1
11
10.4230/DagSemProc.09281.4
article
Minimax Trees in Linear Time with Applications
Gawrychowski, Pawel
Gagie, Travis
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09281/DagSemProc.09281.4/DagSemProc.09281.4.pdf
Data structures
data compression
prefix-free coding
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2009-11-10
9281
1
19
10.4230/DagSemProc.09281.5
article
Pattern matching with don't cares and few errors
Clifford, Raphael
Efremo, Klim
Porat, Ely
Rotschild, Amir
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09281/DagSemProc.09281.5/DagSemProc.09281.5.pdf
Prime Numbers
Group Testing
Streaming
Pattern Matching
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2009-11-10
9281
1
5
10.4230/DagSemProc.09281.6
article
Rounds in Combinatorial Search
Wiener, Gábor
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09281/DagSemProc.09281.6/DagSemProc.09281.6.pdf
Search
group testing
adaptiveness
hypergraph
trace
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2009-11-10
9281
1
16
10.4230/DagSemProc.09281.7
article
Some Aspects of Finite State Channel related to Hidden Markov Process
Kobayashi, Kingo
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09281/DagSemProc.09281.7/DagSemProc.09281.7.pdf
Finite state channel
Hidden Markov source
Gilbert-Elliot channel
Trapdoor Channel