Reconstructing Set Partitions

Colloque avec actes et comité de lecture.We study the following combinatorial search problem: Reconstruct an unknown partition of the set [n]={1,...,n} into at most K disjoint non-empty subsets (classes) by making queries about subsets $Q_i \subseteq [n]$ such that the query returns the number of classes represented in $Q_i$. The goal is to reconstruct the whole partition with as few queries as possible. We also consider a variant of the problem where a representative of each class should be found without necessarily reconstructing the whole partition. Besides its theoretical interest, the problem has practical applications. Paper \cite{SBAW-RECOMB97} considers a physical mapping method based on hybridizing probes to chromosomes using the FISH technology. Under some reasonable assumptions, the method amounts to finding a partition of probes determined by the chromosome they hybridize to, and actually corresponds to the above formalization

Optimal Reconstruction of Graphs under the Additive Model

Article dans revue scientifique avec comité de lecture.We study the problem of reconstructing unknown graphs under the additive combinatorial search model. The main result concerns the reconstruction of {\em bounded degree} \/graphs, i.e.\ graphs with the degree of all vertices bounded by a constant $d$. We show that such graphs can be reconstructed in $O(dn)$ non--adaptive queries, which matches the information--theoretic lower bound. The proof is based on the technique of se\-pa\-rating matrices. A central result here is a new upper bound for a general class of separating matrices. As a particular case, we obtain a tight upper bound for the class of $d$--separating matrices, which settles an open question stated by Lindström in~\cite{Lindstrom75}. Finally, we consider several particular classes of graphs. We show how an optimal non--adaptive solution of $O(n^2/\log n)$ queries for general graphs can be obtained. We also prove that trees with unbounded vertex degree can be reconstructed in a linear number of queries by a non--adaptive algorithm

Graph Reconstruction via Distance Oracles

We study the problem of reconstructing a hidden graph given access to a distance oracle. We design randomized algorithms for the following problems: reconstruction of a degree bounded graph with query complexity $\tilde{O}(n^{3/2})$; reconstruction of a degree bounded outerplanar graph with query complexity $\tilde{O}(n)$; and near-optimal approximate reconstruction of a general graph

Brazilian andforeign cesareas in frontier city: robson classification / Cesáreas de brasileiras e estrangeiras em município de fronteira: classificação de robson

Objetivo: analisar a incidência de cesáreas e as condições clínicas de recém-nascidos de mães brasileiras e estrangeiras conforme a classificação de Robson. Método: estudo de corte transversal, retrospectivo e quantitativo, realizado em 2017 e 2018 em Foz do Iguaçu-PR. Foram incluídas mulheres que tiveram parto entre 2012 a 2016 (n=21.129). Para análise realizou o teste de associação Qui-Quadrado ou o teste G com o nível de significância de 5%. Resultados: a incidência de cesáreas foi de 46%. O grupo de Robson que mais contribuiu foi o 5 e grupos que se mostraram expressivos em relação a escores de Apgar inferior a 7 foram 5, 8, 9 e 10. Para estas mulheres, a necessidade de encaminhamento para cuidados intensivos foi mais expressiva para recém-nascidos do grupo 10. Conclusão: a classificação de Robson é importante para gestão clínica, sendo que o grupo 5 apresenta fatores que reduzem a chance de parto vaginal.

Cuidados com o recém-nascido em ambiente hospitalar: oportunidades de apoio e orientações

Objetivo: Analisar as orientações e o apoio profissional para o cuidado do recémnascido em ambiente hospitalar em três regionais de saúde do estado do Paraná. Método: Estudo analítico, transversal, desenvolvido em 2017 e 2018, em três Regionais de Saúde do Paraná, por meio de inquérito com 1.270 puérperas no alojamento conjunto. Para análise realizou-se teste t de Student com 95% de confiabilidade e teste exato de Fisher (

On the Power of Additive Combinatorial Search Model

We consider two generic problems of combinatorial search under the additive model. The first one is the problem of reconstructing bounded-weight vectors. We establish an optimal upper bound and observe that it unifies many known results for coin-weighing problems. The developed technique provides a basis for the graph reconstruction problem. Optimal upper bound is proven for the class of k-degenerate graphs

Recherche combinatoire : problèmes de pesage, reconstruction de graphes et applications

Texte intégral accessible uniquement aux membres de l'Université de LorraineNot availableLa recherche combinatoire est une branche de l'algorithmique combinatoire qui est étroitement liée avec d'autres domaines des mathématiques et de l'informatique, tels que l'étude de la complexité d'algorithmes, la théorie des graphes, la théorie des nombres, la théorie des ensembles extrémaux. En termes très généraux, la recherche combinatoire étudié les problèmes d'identification d'un objet inconnu dans un ensemble d'objets à l'aide de questions indirectes sur cet objet. Les méthodes de la recherche combinatoire trouvent de nombreuses applications pratiques dans les domaines de la biologie, la médecine, la conception de réseaux, et d'autres. Le thème central de la thèse est le modèle additif en recherche combinatoire. Nous étudions la puissance de ce modèle en l'appliquant à quelques problèmes classiques de recherche combinatoire. Trois familles de problèmes sont considérées : les problèmes de pesage de monnaies, le problème de reconstruction de graphes d'une classe donnée et le problème de reconstruction de partitions. Pour les problèmes de reconstruction de graphes et de pesage, nous examinons les résultats connus et démontrons de nouveaux résultats plus généraux. Un des résultats les plus importants est l'obtention d'une borne supérieure pour le problème de reconstruction de vecteurs à poids borné. Nous introduisons également le problème de reconstruction de partitions, pour lequel nous développons des algorithmes efficaces dont nous analysons la complexit

Reconstructing a Hamiltonian Circuit by Querying the Graph: Application to DNA Physical Mapping

This paper studies three mathematical models of the multiplex PCR method of genome physical mapping described in [12]. The models are expressed as combinatorial group testing problems of finding an unknown Hamiltonian circuit in the complete graph by means of queries of different type. For each model, an efficient algorithm is proposed that matches asymptotically the information-theoretic lower bound. Keywords: genome physical mapping, combinatorial group testing, algorithms, asymptotic complexity. 1 Introduction 1.1 Biological Motivation This paper studies several mathematical models of the multiplex PCR method of genome physical mapping described in [12]. Physical mapping is the central stage in genome exploration which consists in creating some landmarks or tags throughout the DNA molecule. These landmarks are some specific nucleotide sequences associated with their positions on the molecule. They are usually obtained through the process of cloning which allows to extract some fra..

Optimal Reconstruction of Graphs Under the Additive Model

We study the problem of combinatorial search for graphs under the additive model. The main result concerns the reconstruction of bounded degree graphs, i.e. graphs with the degree of all vertices bounded by a constant d. We show that such graphs can be reconstructed in O(dn) non-adaptive queries, that matches the information-theoretic lower bound. The proof is based on the technique of separating matrices. In particular, a new upper bound is obtained for d-separating matrices, that settles an open question stated by Lindstr#m in [16]. Finally, we consider several particular classes of graphs. We show how an optimal non-adaptive solution of O(n²/log n) queries for general graphs can be obtained