No description available.

<p>Modular decompositions of protein interaction networks can be used to identify modules of cooperating proteins. The biological plausibility off these modules might be questioned though. This report describes how a modular decomposition can be completed with semantic information in the visual representation. Possible methods for creating modules of functionally related proteins are also proposed in this work. The results show that such modules, with advantage can be combined with modules from a graph decomposition, to find proteins that are likely to cooperate to perform certain functions in organisms</p>

No description available.

Modular decompositions of protein interaction networks can be used to identify modules of cooperating proteins. The biological plausibility off these modules might be questioned though. This report describes how a modular decomposition can be completed with semantic information in the visual representation. Possible methods for creating modules of functionally related proteins are also proposed in this work. The results show that such modules, with advantage can be combined with modules from a graph decomposition, to find proteins that are likely to cooperate to perform certain functions in organisms

PIGA est un outil permettant de détecter les comportements malicieux par analyse de trace système. Pour cela, il utilise des signatures représentant les comportements violant une ou plusieurs propriétés de sécurité définies dans la politique. Les signatures sont générées à partir de graphes modélisant les opérations entre les différentes entités du système et sont stockées en mémoire pendant la détection d’intrusion. Cette base de signatures peut atteindre une taille de plusieurs Mo et ainsi réduire les performances du système lorsque la détection d’intrusion est active. Durant cette thèse, nous avons mis en place plusieurs méthodes pour réduire la mémoire nécessaire pour stocker les signatures, tout en préservant leur qualité. La première méthode présentée est basée sur la décomposition modulaire des graphes. Nous avons utilisé cet outil de la théorie des graphes pour réduire la taille du graphe et, ainsi, diminuer le nombre de signatures, ainsi que leur longueur. Appliquée à des propriétés de confidentialité sur un système servant de passerelle, cette méthode divise par 20 le nombre de signatures générées. La seconde méthode réduit directement la base de signatures en supprimant des signatures inutiles lorsque PIGA est en mode IPS. Appliquée sur les mêmes propriétés, cette méthode divise par 5 le nombre de signatures générées. En utilisant les deux méthodes, on divise le nombre de signatures par plus de 50. Ensuite, nous avons adapté le mécanisme de détection afin d’utiliser les nouvelles signatures générées. Les expérimentations que nous avons effectuées montrent que notre système est équivalent à l’ancien système. De plus, nous avons réduit le temps de réponse de PIGA. / PIGA is a tool for detecting malicious behaviour by analysing system activity. This tool uses signatures representing illegal behaviours that violate security properties defined in the policy. The signatures are generated from graphs modelling the operation between different system entities and stored in the memory during the intrusion detection. The signature base can take up several MB (Megabytes). This will reduce system performance when the intrusion detection is running. During this thesis, we set up two methods to reduce the memory used to store the signatures while also preserving their quality. The first method is based on the modular decomposition of graphs. We used this notion of graph theory to reduce the size of the graph and lower the number and length of signatures. Applied to confidentiality properties on a gateway system, this method divides by 20 the number of generated signature. The second method reduces directly the signature base by deleting useless signatures when PIGA is used as an IPS. Applied to the same properties, this method divides by 5 the number of generated signatures. Using both methods together, the number of signatures is divided by more than 50. Next, we adapted the detection mechanism to use the new generated signatures. The experiments show that the new mechanism detects the same illegal behaviours detected by the previous one. Furthermore, we reduced the response time of PIGA.

This thesis presents the first sub-quadratic circle graph recognition algorithm, and develops improved algorithms for two important hierarchical decomposition schemes: modular decomposition and split decomposition. The modular decomposition algorithm results from unifying two different approaches previously employed to solve the problem: divide-and-conquer and factorizing permutations. It runs in linear-time, and is straightforward in its understanding, correctness, and implementation. It merely requires a collection of trees and simple traversals of these trees. The split-decomposition algorithm is similar in being straightforward in its understanding and correctness. An efficient implementation of the algorithm is described that uses the union-find data-structure. A novel charging argument is used to prove the running-time. The algorithm is the first to use the recent reformulation of split decomposition in terms of graph-labelled trees. This facilitates its extension to circle graph recognition. In particular, it allows us to efficiently apply a new lexicographic breadth-first search characterization of circle graphs developed in the thesis. Lexicographic breadth-first search is additionally responsible for the efficiency of the split decomposition algorithm, and contributes to the simplicity of the modular decomposition algorithm.

This thesis presents the first sub-quadratic circle graph recognition algorithm, and develops improved algorithms for two important hierarchical decomposition schemes: modular decomposition and split decomposition. The modular decomposition algorithm results from unifying two different approaches previously employed to solve the problem: divide-and-conquer and factorizing permutations. It runs in linear-time, and is straightforward in its understanding, correctness, and implementation. It merely requires a collection of trees and simple traversals of these trees. The split-decomposition algorithm is similar in being straightforward in its understanding and correctness. An efficient implementation of the algorithm is described that uses the union-find data-structure. A novel charging argument is used to prove the running-time. The algorithm is the first to use the recent reformulation of split decomposition in terms of graph-labelled trees. This facilitates its extension to circle graph recognition. In particular, it allows us to efficiently apply a new lexicographic breadth-first search characterization of circle graphs developed in the thesis. Lexicographic breadth-first search is additionally responsible for the efficiency of the split decomposition algorithm, and contributes to the simplicity of the modular decomposition algorithm.

Diese Arbeit leistet Beiträge im Bereich der deskriptiven Komplexitätstheorie. Zunächst beschäftigen wir uns mit der ungelösten Frage, ob es eine Logik gibt, welche die Klasse der Polynomialzeit-Eigenschaften (PTIME) charakterisiert. Wir betrachten Graphklassen, die unter induzierten Teilgraphen abgeschlossen sind. Auf solchen Graphklassen lässt sich die 1976 von Gallai eingeführte modulare Zerlegung anwenden. Graphen, die durch modulare Zerlegung nicht zerlegbar sind, heißen prim. Wir stellen ein neues Werkzeug vor: das Modulare Zerlegungstheorem. Es reduziert (definierbare) Kanonisierung einer Graphklasse C auf (definierbare) Kanonisierung der Klasse aller primen Graphen aus C, die mit binären Relationen auf einer linear geordneten Menge gefärbt sind. Mit Hilfe des Modularen Zerlegungstheorems zeigen wir, dass Fixpunktlogik mit Zählen (FP+C) PTIME auf der Klasse aller Permutationsgraphen und auf der Klasse aller chordalen Komparabilitätsgraphen charakterisiert. Wir beweisen zudem, dass modulare Zerlegungsbäume in Symmetrisch-Transitive-Hüllen-Logik mit Zählen (STC+C) definierbar und damit in logarithmischem Platz berechenbar sind. Weiterhin definieren wir eine neue Logik für die Komplexitätsklasse Logarithmischer Platz (LOGSPACE). Wir erweitern die Logik erster Stufe mit Zählen um einen Operator, der eine in logarithmischem Platz berechenbare Form der Rekursion erlaubt. Die resultierende Logik LREC ist ausdrucksstärker als die Deterministisch-Transitive-Hüllen-Logik mit Zählen (DTC+C) und echt in FP+C enthalten. Wir zeigen, dass LREC LOGSPACE auf gerichteten Bäumen charakterisiert. Zudem betrachten wir eine Erweiterung LREC= von LREC, die sich gegenüber LREC durch bessere Abschlusseigenschaften auszeichnet und im Gegensatz zu LREC ausdrucksstärker als die Symmetrisch-Transitive-Hüllen-Logik (STC) ist. Wir beweisen, dass LREC= LOGSPACE sowohl auf der Klasse der Intervallgraphen als auch auf der Klasse der chordalen klauenfreien Graphen charakterisiert. / This theses is making contributions to the field of descriptive complexity theory. First, we look at the main open problem in this area: the question of whether there exists a logic that captures polynomial time (PTIME). We consider classes of graphs that are closed under taking induced subgraphs. For such graph classes, an effective graph decomposition, called modular decomposition, was introduced by Gallai in 1976. The graphs that are non-decomposable with respect to modular decomposition are called prime. We present a tool, the Modular Decomposition Theorem, that reduces (definable) canonization of a graph class C to (definable) canonization of the class of prime graphs of C that are colored with binary relations on a linearly ordered set. By an application of the Modular Decomposition Theorem, we show that fixed-point logic with counting (FP+C) captures PTIME on the class of permutation graphs and the class of chordal comparability graphs. We also prove that the modular decomposition tree is definable in symmetric transitive closure logic with counting (STC+C), and therefore, computable in logarithmic space. Further, we introduce a new logic for the complexity class logarithmic space (LOGSPACE). We extend first-order logic with counting by a new operator that allows it to formalize a limited form of recursion which can be evaluated in logarithmic space. We prove that the resulting logic LREC is strictly more expressive than deterministic transitive closure logic with counting (DTC+C) and that it is strictly contained in FP+C. We show that LREC captures LOGSPACE on the class of directed trees. We also study an extension LREC= of LREC that has nicer closure properties and that, unlike LREC, is more expressive than symmetric transitive closure logic (STC). We prove that LREC= captures LOGSPACE on the class of interval graphs and on the class of chordal claw-free graphs.

This thesis focuses mainly on the Maximum Independent Set (MIS) problem. Some related graph theoretical combinatorial problems are also considered. As these problems are generally NP-hard, we study their complexity in hereditary graph classes, i.e. graph classes defined by a set F of forbidden induced subgraphs. We revise the literature about the issue, for example complexity results, applications, and techniques tackling the problem. Through considering some general approach, we exhibit several cases where the problem admits a polynomial-time solution. More specifically, we present polynomial-time algorithms for the MIS problem in: + some subclasses of $S_{2;j;k}$-free graphs (thus generalizing the classical result for $S_{1;2;k}$-free graphs); + some subclasses of $tree_{k}$-free graphs (thus generalizing the classical results for subclasses of P5-free graphs); + some subclasses of $P_{7}$-free graphs and $S_{2;2;2}$-free graphs; and various subclasses of graphs of bounded maximum degree, for example subcubic graphs. Our algorithms are based on various approaches. In particular, we characterize augmenting graphs in a subclass of $S_{2;k;k}$-free graphs and a subclass of $S_{2;2;5}$-free graphs. These characterizations are partly based on extensions of the concept of redundant set [125]. We also propose methods finding augmenting chains, an extension of the method in [99], and finding augmenting trees, an extension of the methods in [125]. We apply the augmenting vertex technique, originally used for $P_{5}$-free graphs or banner-free graphs, for some more general graph classes. We consider a general graph theoretical combinatorial problem, the so-called Maximum -Set problem. Two special cases of this problem, the so-called Maximum F-(Strongly) Independent Subgraph and Maximum F-Induced Subgraph, where F is a connected graph set, are considered. The complexity of the Maximum F-(Strongly) Independent Subgraph problem is revised and the NP-hardness of the Maximum F-Induced Subgraph problem is proved. We also extend the augmenting approach to apply it for the general Maximum Π -Set problem. We revise on classical graph transformations and give two unified views based on pseudo-boolean functions and αff-redundant vertex. We also make extensive uses of α-redundant vertices, originally mainly used for $P_{5}$-free graphs, to give polynomial solutions for some subclasses of $S_{2;2;2}$-free graphs and $tree_{k}$-free graphs. We consider some classical sequential greedy heuristic methods. We also combine classical algorithms with αff-redundant vertices to have new strategies of choosing the next vertex in greedy methods. Some aspects of the algorithms, for example forbidden induced subgraph sets and worst case results, are also considered. Finally, we restrict our attention on graphs of bounded maximum degree and subcubic graphs. Then by using some techniques, for example ff-redundant vertex, clique separator, and arguments based on distance, we general these results for some subclasses of $S_{i;j;k}$-free subcubic graphs.

This thesis focuses mainly on the Maximum Independent Set (MIS) problem. Some related graph theoretical combinatorial problems are also considered. As these problems are generally NP-hard, we study their complexity in hereditary graph classes, i.e. graph classes defined by a set F of forbidden induced subgraphs. We revise the literature about the issue, for example complexity results, applications, and techniques tackling the problem. Through considering some general approach, we exhibit several cases where the problem admits a polynomial-time solution. More specifically, we present polynomial-time algorithms for the MIS problem in: + some subclasses of $S_{2;j;k}$-free graphs (thus generalizing the classical result for $S_{1;2;k}$-free graphs); + some subclasses of $tree_{k}$-free graphs (thus generalizing the classical results for subclasses of P5-free graphs); + some subclasses of $P_{7}$-free graphs and $S_{2;2;2}$-free graphs; and various subclasses of graphs of bounded maximum degree, for example subcubic graphs. Our algorithms are based on various approaches. In particular, we characterize augmenting graphs in a subclass of $S_{2;k;k}$-free graphs and a subclass of $S_{2;2;5}$-free graphs. These characterizations are partly based on extensions of the concept of redundant set [125]. We also propose methods finding augmenting chains, an extension of the method in [99], and finding augmenting trees, an extension of the methods in [125]. We apply the augmenting vertex technique, originally used for $P_{5}$-free graphs or banner-free graphs, for some more general graph classes. We consider a general graph theoretical combinatorial problem, the so-called Maximum -Set problem. Two special cases of this problem, the so-called Maximum F-(Strongly) Independent Subgraph and Maximum F-Induced Subgraph, where F is a connected graph set, are considered. The complexity of the Maximum F-(Strongly) Independent Subgraph problem is revised and the NP-hardness of the Maximum F-Induced Subgraph problem is proved. We also extend the augmenting approach to apply it for the general Maximum Π -Set problem. We revise on classical graph transformations and give two unified views based on pseudo-boolean functions and αff-redundant vertex. We also make extensive uses of α-redundant vertices, originally mainly used for $P_{5}$-free graphs, to give polynomial solutions for some subclasses of $S_{2;2;2}$-free graphs and $tree_{k}$-free graphs. We consider some classical sequential greedy heuristic methods. We also combine classical algorithms with αff-redundant vertices to have new strategies of choosing the next vertex in greedy methods. Some aspects of the algorithms, for example forbidden induced subgraph sets and worst case results, are also considered. Finally, we restrict our attention on graphs of bounded maximum degree and subcubic graphs. Then by using some techniques, for example ff-redundant vertex, clique separator, and arguments based on distance, we general these results for some subclasses of $S_{i;j;k}$-free subcubic graphs.