On the minimum leaf number of cubic graphs

The \emph{minimum leaf number} $\hbox{ml} (G)$ of a connected graph $G$ is defined as the minimum number of leaves of the spanning trees of $G$. We present new results concerning the minimum leaf number of cubic graphs: we show that if $G$ is a connected cubic graph of order $n$, then $\mathrm{ml}(G) \leq \frac{n}6 + \frac13$, improving on the best known result in [Inf. Process. Lett. 105 (2008) 164-169] and proving the conjecture in [Electron. J. Graph Theory and Applications 5 (2017) 207-211]. We further prove that if $G$ is also 2-connected, then $\mathrm{ml}(G) \leq \frac{n}{6.53}$, improving on the best known bound in [Math. Program., Ser. A 144 (2014) 227-245]. We also present new conjectures concerning the minimum leaf number of several types of cubic graphs and examples showing that the bounds of the conjectures are best possible.Comment: 17 page

A Requirements-Based Exploration of Open-Source Software Development Projects – Towards a Natural Language Processing Software Analysis Framework

Open source projects do have requirements; they are, however, mostly informal, text descriptions found in requests, forums, and other correspondence. Understanding such requirements provides insight into the nature of open source projects. Unfortunately, manual analysis of natural language requirements is time-consuming, and for large projects, error-prone. Automated analysis of natural language requirements, even partial, will be of great benefit. Towards that end, I describe the design and validation of an automated natural language requirements classifier for open source software development projects. I compare two strategies for recognizing requirements in open forums of software features. The results suggest that classifying text at the forum post aggregation and sentence aggregation levels may be effective. Initial results suggest that it can reduce the effort required to analyze requirements of open source software development projects. Software development organizations and communities currently employ a large number of software development techniques and methodologies. This implied complexity is also enhanced by a wide range of software project types and development environments. The resulting lack of consistency in the software development domain leads to one important challenge that researchers encounter while exploring this area: specificity. This results in an increased difficulty of maintaining a consistent unit of measure or analysis approach while exploring a wide variety of software development projects and environments. The problem of specificity is more prominently exhibited in an area of software development characterized by a dynamic evolution, a unique development environment, and a relatively young history of research when compared to traditional software development: the open-source domain. While performing research on open source and the associated communities of developers, one can notice the same challenge of specificity being present in requirements engineering research as in the case of closed-source software development. Whether research is aimed at performing longitudinal or cross-sectional analyses, or attempts to link requirements to other aspects of software development projects and their management, specificity calls for a flexible analysis tool capable of adapting to the needs and specifics of the explored context. This dissertation covers the design, implementation, and evaluation of a model, a method, and a software tool comprising a flexible software development analysis framework. These design artifacts use a rule-based natural language processing approach and are built to meet the specifics of a requirements-based analysis of software development projects in the open-source domain. This research follows the principles of design science research as defined by Hevner et. al. and includes stages of problem awareness, suggestion, development, evaluation, and results and conclusion (Hevner et al. 2004; Vaishnavi and Kuechler 2007). The long-term goal of the research stream stemming from this dissertation is to propose a flexible, customizable, requirements-based natural language processing software analysis framework which can be adapted to meet the research needs of multiple different types of domains or different categories of analyses

A Naive Based Approach for Mapping Two ADL Models

In software engineering we have identified and described the model correspondence problem To Describe system architecture and artifacts uses models and diagrams Models contains series of versions To understand how versions correspondence are difficult So we designed a framework based on Search and Ammolite algorithms which can cardinally finds the correspondence software models Models are represented as graphs whose nodes have attributes name edge label connections For a given diagram pair it performs different individual matches such as pair-wise match Split-Merge Match and Drop match and then combine all matches together to design a ADL model Every ADL Model has its correspondence score for rating quality candidates To find best Correspondence among the given ADL models uses Search and Ammolite Algorithm

Exploring the impact of software requirements on system-wide goals: a method using satisfaction arguments and i* goal modelling

This paper describes the application of requirements engineering concepts to support the analysis of the impact of new software systems on system-wide goals. Requirements on a new or revised software component of a socio-technical system not only have implications on the goals of the subsystem itself, but they also impact upon the goals of the existing integrated system. In industries such as air traffic management and healthcare, impacts need to be identified and demonstrated in order to assess concerns such as risk, safety, and accuracy. A method called PiLGRIM was developed which integrates means-end relationships within goal modelling with knowledge associated with the application domain. The relationship between domain knowledge and requirements, as described in a satisfaction argument, adds traceability rationale to help determine the impacts of new requirements across a network of heterogeneous actors. We report procedures that human analysts follow to use the concepts of satisfaction arguments in a software tool for i* goal modelling. Results were demonstrated using models and arguments developed in two case studies, each featuring a distinct socio-technical system – a new controlled airspace infringement detection tool for NATS (the UK's air navigation service provider), and a new version of the UK’s HIV/AIDS patient reporting system. Results provided evidence towards our claims that the conceptual integration of i* and satisfaction arguments is usable and useful to human analysts, and that the PiLGRIM impact analysis procedures and tool support are effective and scalable to model and analyse large and complex socio-technical systems

Algorithmic Graph Theory

The main focus of this workshop was on mathematical techniques needed for the development of efficient solutions and algorithms for computationally difficult graph problems. The techniques studied at the workshhop included: the probabilistic method and randomized algorithms, approximation and optimization, structured families of graphs and approximation algorithms for large problems. The workshop Algorithmic Graph Theory was attended by 46 participants, many of them being young researchers. In 15 survey talks an overview of recent developments in Algorithmic Graph Theory was given. These talks were supplemented by 10 shorter talks and by two special sessions

Hypohamiltonian and almost hypohamiltonian graphs

This Dissertation is structured as follows. In Chapter 1, we give a short historical overview and define fundamental concepts. Chapter 2 contains a clear narrative of the progress made towards finding the smallest planar hypohamiltonian graph, with all of the necessary theoretical tools and techniques--especially Grinberg's Criterion. Consequences of this progress are distributed over all sections and form the leitmotif of this Dissertation. Chapter 2 also treats girth restrictions and hypohamiltonian graphs in the context of crossing numbers. Chapter 3 is a thorough discussion of the newly introduced almost hypohamiltonian graphs and their connection to hypohamiltonian graphs. Once more, the planar case plays an exceptional role. At the end of the chapter, we study almost hypotraceable graphs and Gallai's problem on longest paths. The latter leads to Chapter 4, wherein the connection between hypohamiltonicity and various problems related to longest paths and longest cycles are presented. Chapter 5 introduces and studies non-hamiltonian graphs in which every vertex-deleted subgraph is traceable, a class encompassing hypohamiltonian and hypotraceable graphs. We end with an outlook in Chapter 6, where we present a selection of open problems enriched with comments and partial results