Rectangular Layouts and Contact Graphs

Contact graphs of isothetic rectangles unify many concepts from applications including VLSI and architectural design, computational geometry, and GIS. Minimizing the area of their corresponding {\em rectangular layouts} is a key problem. We study the area-optimization problem and show that it is NP-hard to find a minimum-area rectangular layout of a given contact graph. We present O(n)-time algorithms that construct $O(n^2)$-area rectangular layouts for general contact graphs and $O(n\log n)$-area rectangular layouts for trees. (For trees, this is an $O(\log n)$-approximation algorithm.) We also present an infinite family of graphs (rsp., trees) that require $\Omega(n^2)$ (rsp., $\Omega(n\log n)$) area. We derive these results by presenting a new characterization of graphs that admit rectangular layouts using the related concept of {\em rectangular duals}. A corollary to our results relates the class of graphs that admit rectangular layouts to {\em rectangle of influence drawings}.Comment: 28 pages, 13 figures, 55 references, 1 appendi

Identifying the underlying structure and dynamic interactions in a voting network

We analyse the structure and behaviour of a specific voting network using a dynamic structure-based methodology which draws on Q-Analysis and social network theory. Our empirical focus is on the Eurovision Song Contest over a period of 20 years. For a multicultural contest of this kind, one of the key questions is how the quality of a song is judged and how voting groups emerge. We investigate structures that may identify the winner based purely on the topology of the network. This provides a basic framework to identify what the characteristics associated with becoming a winner are, and may help to establish a homogenous criterion for subjective measures such as quality. Further, we measure the importance of voting cliques, and present a dynamic model based on a changing multidimensional measure of connectivity in order to reveal the formation of emerging community structure within the contest. Finally, we study the dynamic behaviour exhibited by the network in order to understand the clustering of voting preferences and the relationship between local and global properties.Comment: 20 pages, 10 figures, 3 tables, submitted to Physica

Automatic synthesis of analog layout : a survey

A review of recent research in the automatic synthesis of physical geometry for analog integrated circuits is presented. On introduction, an explanation of the difficulties involved in analog layout as opposed to digital layout is covered. Review of the literature then follows. Emphasis is placed on the exposition of general methods for addressing problems specific to analog layout, with the details of specific systems only being given when they surve to illustrate these methods well. The conclusion discusses problems remaining and offers a prediction as to how technology will evolve to solve them. It is argued that although progress has been and will continue to be made in the automation of analog IC layout, due to fundamental differences in the nature of analog IC design as opposed to digital design, it should not be expected that the level of automation of the former will reach that of the latter any time soon

``Sum over Surfaces'' form of Loop Quantum Gravity

We derive a spacetime formulation of quantum general relativity from (hamiltonian) loop quantum gravity. In particular, we study the quantum propagator that evolves the 3-geometry in proper time. We show that the perturbation expansion of this operator is finite and computable order by order. By giving a graphical representation a' la Feynman of this expansion, we find that the theory can be expressed as a sum over topologically inequivalent (branched, colored) 2d surfaces in 4d. The contribution of one surface to the sum is given by the product of one factor per branching point of the surface. Therefore branching points play the role of elementary vertices of the theory. Their value is determined by the matrix elements of the hamiltonian constraint, which are known. The formulation we obtain can be viewed as a continuum version of Reisenberger's simplicial quantum gravity. Also, it has the same structure as the Ooguri-Crane-Yetter 4d topological field theory, with a few key differences that illuminate the relation between quantum gravity and TQFT. Finally, we suggests that certain new terms should be added to the hamiltonian constraint in order to implement a ``crossing'' symmetry related to 4d diffeomorphism invariance.Comment: Seriously revised version. LaTeX, with revtex and epsfi

Object linking in repositories

This topic is covered in three sections. The first section explores some of the architectural ramifications of extending the Eichmann/Atkins lattice-based classification scheme to encompass the assets of the full life cycle of software development. A model is considered that provides explicit links between objects in addition to the edges connecting classification vertices in the standard lattice. The second section gives a description of the efforts to implement the repository architecture using a commercially available object-oriented database management system. Some of the features of this implementation are described, and some of the next steps to be taken to produce a working prototype of the repository are pointed out. In the final section, it is argued that design and instantiation of reusable components have competing criteria (design-for-reuse strives for generality, design-with-reuse strives for specificity) and that providing mechanisms for each can be complementary rather than antagonistic. In particular, it is demonstrated how program slicing techniques can be applied to customization of reusable components

TimeLighting: Guidance-enhanced Exploration of 2D Projections of Temporal Graphs

In temporal (or event-based) networks, time is a continuous axis, with real-valued time coordinates for each node and edge. Computing a layout for such graphs means embedding the node trajectories and edge surfaces over time in a 2D + t space, known as the space-time cube. Currently, these space-time cube layouts are visualized through animation or by slicing the cube at regular intervals. However, both techniques present problems ranging from sub-par performance on some tasks to loss of precision. In this paper, we present TimeLighting, a novel visual analytics approach to visualize and explore temporal graphs embedded in the space-time cube. Our interactive approach highlights the node trajectories and their mobility over time, visualizes node "aging", and provides guidance to support users during exploration. We evaluate our approach through two case studies, showing the system's efficacy in identifying temporal patterns and the role of the guidance features in the exploration process.Comment: Appears in the Proceedings of the 31st International Symposium on Graph Drawing and Network Visualization (GD 2023

Student Understanding of the Definite Integral When Solving Calculus Volume Problems

The concept of integration appears in many different scientific fields, and students’ understanding of and ability to use the definite integral in applications is important to success in their STEM (science, technology, engineering, and mathematics) classes. One of the first types of application problems that students encounter is finding the volume of a solid using the definite integral. How students approach these problems and how they use the definite integral to find volumes can have an impact on their future use and understanding of the definite integral. This study involves a deep and thorough investigation of how ten students understand the definite integral when solving two types of volume problems: revolution volume problems and non-revolution volume problems. First, using the Riemann Integral Framework (Sealey, 2014), I analyzed how students understood the underlying structure of the definite integral when solving revolution volume problems. Using Piaget’s (1971) learning theory of structuralism, I then examined how students’ understanding of the familiar revolution volume problems affected and influenced their solving of novel non-revolution volume problems. The data was collected via one-on-one interviews where students worked through three different volume problems and discussed their thoughts and work. The findings of this study can be summarized in three parts. First, students can build symbolically correct revolution volume problem integrals without understanding conceptually why their integral is correct. These students relied on memorized formulas without understanding why the formulas worked. Second, students’ memorized formulas for revolution volume problems break down when attempting to apply them to non-revolution volume problems. Third, display of or development of conceptual understanding emerged either when being asked deliberate and probing questions about their revolution volume integrals or separately while solving the non-revolution volume problems. The students who were able to discuss their revolution volume problem integrals conceptually accurately had continued success throughout the interview. Revolution volume problems are a standard application of the definite integral and many textbooks spend a lot of time and pages on them, but as this study has shown, using revolution volume problems alone or without asking conceptual questions is not enough to ensure understanding of how definite integrals work to solve volume problems. Non-revolution volume problems provide an environment that is resistant to students’ inclinations to memorize formulas and provides a greater opportunity for students to attend to the underlying structure of the definite integral

The Stores Model of Code Cognition

Program comprehension is perhaps one of the oldest topics within the psychology of programming. It addresses a central issue: how programmers work with and manipulate source code to construct effective software systems. Models can play an important role in understanding the challenges developers and engineers contend with. This paper presents a model of program comprehension, or code cognition, which has been derived from literature found within the disciplines of computing and psychology. Drawing on direct experimentation, this paper argues that a model of code cognition should take account of the visual, spatial and linguistic abilities of developers. The strengths and weaknesses of this model are discussed and further research directions presented