Practical and Efficient Split Decomposition via Graph-Labelled Trees

Split decomposition of graphs was introduced by Cunningham (under the name join decomposition) as a generalization of the modular decomposition. This paper undertakes an investigation into the algorithmic properties of split decomposition. We do so in the context of graph-labelled trees (GLTs), a new combinatorial object designed to simplify its consideration. GLTs are used to derive an incremental characterization of split decomposition, with a simple combinatorial description, and to explore its properties with respect to Lexicographic Breadth-First Search (LBFS). Applying the incremental characterization to an LBFS ordering results in a split decomposition algorithm that runs in time $O(n+m)\alpha(n+m)$, where $\alpha$ is the inverse Ackermann function, whose value is smaller than 4 for any practical graph. Compared to Dahlhaus' linear-time split decomposition algorithm [Dahlhaus'00], which does not rely on an incremental construction, our algorithm is just as fast in all but the asymptotic sense and full implementation details are given in this paper. Also, our algorithm extends to circle graph recognition, whereas no such extension is known for Dahlhaus' algorithm. The companion paper [Gioan et al.] uses our algorithm to derive the first sub-quadratic circle graph recognition algorithm

Hierarchical incremental class learning with reduced pattern training

Hierarchical Incremental Class Learning (HICL) is a new task decomposition method that addresses the pattern classification problem. HICL is proven to be a good classifier but closer examination reveals areas for potential improvement. This paper proposes a theoretical model to evaluate the performance of HICL and presents an approach to improve the classification accuracy of HICL by applying the concept of Reduced Pattern Training (RPT). The theoretical analysis shows that HICL can achieve better classification accuracy than Output Parallelism [1]. The procedure for RPT is described and compared with the original training procedure. RPT reduces systematically the size of the training data set based on the order of sub-networks built. The results from four benchmark classification problems show much promise for the improved model

The modular structure of an ontology: Atomic decomposition

Extracting a subset of a given ontology that captures all the ontology’s knowledge about a specified set of terms is a well-understood task. This task can be based, for instance, on locality-based modules. However, a single module does not allow us to understand neither topicality, connectedness, structure, or superfluous parts of an ontology, nor agreement between actual and intended modeling. The strong logical properties of locality-based modules suggest that the family of all such modules of an ontology can support comprehension of the ontology as a whole. However, extracting that family is not feasible, since the number of localitybased modules of an ontology can be exponential w.r.t. its size. In this paper we report on a new approach that enables us to efficiently extract a polynomial representation of the family of all locality-based modules of an ontology. We also describe the fundamental algorithm to pursue this task, and report on experiments carried out and results obtained.

The imperfect hiding : some introductory concepts and preliminary issues on modularity

In this work we present a critical assessment of some problems and open questions on the debated notion of modularity. Modularity is greatly in fashion nowadays, being often proposed as the new approach to complex artefact production that enables to combine fast innovation pace, enhanced product variety and reduced need for co-ordination. In line with recent critical assessments of the managerial literature on modularity, we sustain that modularity is only one among several arrangements to cope with the complexity inherent in most high-technology artefact production, and by no means the best one. We first discuss relations between modularity and the broader (and much older within economics) notion of division of labour. Then we sustain that a modular approach to labour division aimed at eliminating technological interdependencies between components or phases of a complex production process may have, as a by-product, the creation of other types of interdependencies which may subsequently result in inefficiencies of various types. Hence, the choice of a modular design strategy implies the resolution of various tradeoffs. Depending on how such tradeoffs are solved, different organisational arrangements may be created to cope with ‘residual’ interdependencies. Hence, there is no need to postulate a perfect isomorphism, as some recent literature has proposed, between modularity at the product level and modularity at the organisational level

Slopes for higher rank Artin-Schreier-Witt Towers

We fix a monic polynomial $\bar f(x) \in \mathbb{F}_q[x]$ over a finite field of characteristic $p$, and consider the $\mathbb{Z}_{p^{\ell}}$-Artin-Schreier-Witt tower defined by $\bar f(x)$; this is a tower of curves $\cdots \to C_m \to C_{m-1} \to \cdots \to C_0 =\mathbb{A}^1$, whose Galois group is canonically isomorphic to $\mathbb{Z}_{p^\ell}$, the degree $\ell$ unramified extension of $\mathbb{Z}_p$, which is abstractly isomorphic to $(\mathbb{Z}_p)^\ell$ as a topological group. We study the Newton slopes of zeta functions of this tower of curves. This reduces to the study of the Newton slopes of L-functions associated to characters of the Galois group of this tower. We prove that, when the conductor of the character is large enough, the Newton slopes of the L-function asymptotically form a finite union of arithmetic progressions. As a corollary, we prove the spectral halo property of the spectral variety associated to the $\mathbb{Z}_{p^{\ell}}$-Artin-Schreier-Witt tower. This extends the main result in [DWX] from rank one case $\ell=1$ to the higher rank case $\ell\geq 1$.Comment: 20 page

Supporting the automated generation of modular product line safety cases

Abstract The effective reuse of design assets in safety-critical Software Product Lines (SPL) would require the reuse of safety analyses of those assets in the variant contexts of certification of products derived from the SPL. This in turn requires the traceability of SPL variation across design, including variation in safety analysis and safety cases. In this paper, we propose a method and tool to support the automatic generation of modular SPL safety case architectures from the information provided by SPL feature modeling and model-based safety analysis. The Goal Structuring Notation (GSN) safety case modeling notation and its modular extensions supported by the D-Case Editor were used to implement the method in an automated tool support. The tool was used to generate a modular safety case for an automotive Hybrid Braking System SPL

A survey on algorithmic aspects of modular decomposition

The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important preprocessing step to solve a large number of combinatorial optimization problems. Since the first polynomial time algorithm in the early 70's, the algorithmic of the modular decomposition has known an important development. This paper survey the ideas and techniques that arose from this line of research

Class decomposition for GA-based classifier agents – A Pitt approach

Incremental learning has been widely addressed in the machine learning literature to cope with learning tasks where the learning environment is ever changing or training samples become available over time. However, most research work explores incremental learning with statistical algorithms or neural networks, rather than evolutionary algorithms. The work in this paper employs genetic algorithms (GAs) as basic learning algorithms for incremental learning within one or more classifier agents in a multi-agent environment. Four new approaches with different initialization schemes are proposed. They keep the old solutions and use an “integration” operation to integrate them with new elements to accommodate new attributes, while biased mutation and crossover operations are adopted to further evolve a reinforced solution. The simulation results on benchmark classification data sets show that the proposed approaches can deal with the arrival of new input attributes and integrate them with the original input space. It is also shown that the proposed approaches can be successfully used for incremental learning and improve classification rates as compared to the retraining GA. Possible applications for continuous incremental training and feature selection are also discussed

Strategic perspectives on modularity

In this paper we argue that the debate on modularity has come to a point where a consensus is slowly emerging. However, we also contend that this consensus is clearly technology driven. In particular, no room is left for firm strategies. Typically, technology is considered as an exogenous variable to which firms have no choices but to adapt. Taking a slightly different perspective, our main objective is to offer a conceptual framework enabling to shed light on the role of corporate strategies in the process of modularization. From interviews with academic design engineers, we show that firms often consider product architecture as a critical variable to fit their strategic requirements. Based on design sciences, we build an original approach to product modularity. This approach, which leaves an important space for firms' strategic choices, proves also to seize a large part of the industrial reality of modularity. Our framework, which is a first step towards the consideration of strategies within the framework of modularity, gives an account for the diversity of industrial logics related to product modularization.product modularity ; corporate strategy ; technological determinism