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19
Solving linear arithmetic constraints for user interface applications: Algorithm details
, 1997
"... Linear equality and inequality constraints arise naturally in specifying many aspects of user interfaces, such as requiring that one window be to the left of another, requiring that a pane occupy the leftmost 1/3 of a window, or preferring that an object be contained within a rectangle if possible. ..."
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Cited by 64 (17 self)
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Linear equality and inequality constraints arise naturally in specifying many aspects of user interfaces, such as requiring that one window be to the left of another, requiring that a pane occupy the leftmost 1/3 of a window, or preferring that an object be contained within a rectangle if possible. Current constraint solvers designed for UI applications cannot efficiently handle simultaneous linear equations and inequalities. This is a major limitation. We describe incremental algorithms based on the dual simplex and active set methods that can solve such systems of constraints efficiently.
IPSepCoLa: An incremental procedure for separation constraint layout of graphs
 IEEE TRANSACTIONS ON VISUALISATION AND COMPUTER GRAPHICS
, 2006
"... We extend the popular forcedirected approach to network (or graph) layout to allow separation constraints, which enforce a minimum horizontal or vertical separation between selected pairs of nodes. This simple class of linear constraints is expressive enough to satisfy a wide variety of applicati ..."
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Cited by 27 (12 self)
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We extend the popular forcedirected approach to network (or graph) layout to allow separation constraints, which enforce a minimum horizontal or vertical separation between selected pairs of nodes. This simple class of linear constraints is expressive enough to satisfy a wide variety of applicationspecific layout requirements, including: layout of directed graphs to better show flow; layout with nonoverlapping node labels; and layout of graphs with grouped nodes (called clusters). In the stress majorization forcedirected layout process, separation constraints can be treated as a quadratic programming problem. We give an incremental algorithm based on gradient projection for efficiently solving this problem. The algorithm is considerably faster than using generic constraint optimization techniques and is comparable in speed to unconstrained stress majorization. We demonstrate the utility of our technique with sample data from a number of practical applications including geneactivation networks, terrorist networks and visualization of highdimensional data.
Ultraviolet: A Constraint Satisfaction Algorithm for Interactive Graphics
 Constraints: An International Journal
, 1998
"... . Ultraviolet is a constraint satisfaction algorithm intended for use in interactive graphical applications. It is capable of solving constraints over arbitrary domains using local propagation, and inequality constraints and simultaneous linear equations over the reals. To support this, Ultraviolet ..."
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Cited by 26 (1 self)
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. Ultraviolet is a constraint satisfaction algorithm intended for use in interactive graphical applications. It is capable of solving constraints over arbitrary domains using local propagation, and inequality constraints and simultaneous linear equations over the reals. To support this, Ultraviolet is a hybrid algorithm that allows different subsolvers to be used for different parts of the constraint graph, depending on graph topology and kind of constraints. In addition, Ultraviolet and its subsolvers support plan compilation, producing efficient compiled code that can be evaluated repeatedly to resatisfy a given collection of constraints for different input values. Keywords: constraints, user interfaces, hybrid constraint satisfaction algorithms 1. Introduction Many key aspects of interactive graphical systems can be conveniently described using constraints, including layout and other kinds of geometric relations, consistency between application data and views, consistency of multi...
Schematizing Maps: Simplification of Geographic Shape by Discrete Curve Evolution
 Spatial Cognition II
, 2000
"... Shape simplification in maplike representations is used for two reasons: either to abstract from irrelevant detail to reduce a map user's cognitive load, or to simplify information when a map of a smaller scale is derived from a detailed reference map. We present a method for abstracting simpli ..."
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Cited by 21 (3 self)
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Shape simplification in maplike representations is used for two reasons: either to abstract from irrelevant detail to reduce a map user's cognitive load, or to simplify information when a map of a smaller scale is derived from a detailed reference map. We present a method for abstracting simplified cartographic representations from more accurate spatial data. First, the employed method of discrete curve evolution developed for simplifying perceptual shape characteristics is explained. Specific problems of applying the method to cartographic data are elaborated. An algorithm is presented, which on the one hand simplifies spatial data up to a degree of abstraction intended by the user; and which on the other hand does not violate local spatial ordering between (elements of) cartographic entities, since local arrangement of entities is assumed to be an important spatial knowledge characteristic. The operation of the implemented method is demonstrated using two different examples of cartographic data.
A Numerical Optimization Approach to General Graph Drawing
, 1999
"... Graphs are ubiquitous, finding applications in domains ranging from software engineering to computational biology. While graph theory and graph algorithms are some of the oldest, most studied fields in computer science, the problem of visualizing graphs is comparatively young. This problem, known as ..."
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Cited by 19 (0 self)
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Graphs are ubiquitous, finding applications in domains ranging from software engineering to computational biology. While graph theory and graph algorithms are some of the oldest, most studied fields in computer science, the problem of visualizing graphs is comparatively young. This problem, known as graph drawing, is that of transforming combinatorial graphs into geometric drawings for the purpose of visualization. Most published algorithms for drawing general graphs model the drawing problem with a physical analogy, representing a graph as a system of springs and other physical elements and then simulating the relaxation of this physical system. Solving the graph drawing problem involves both choosing a physical model and then using numerical optimization to simulate the physical system. In this
QOCA: A constraint solving toolkit for interactive graphical applications
 Constraints
, 2002
"... Abstract. We describe an objectoriented constraint solving toolkit, QOCA, designed for interactive graphical applications. It has a simple yet powerful interface based on the metric space model for constraint manipulation. In this model interaction with the constraint solver can occur in three ways ..."
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Cited by 9 (4 self)
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Abstract. We describe an objectoriented constraint solving toolkit, QOCA, designed for interactive graphical applications. It has a simple yet powerful interface based on the metric space model for constraint manipulation. In this model interaction with the constraint solver can occur in three ways: a constraint may be added, a constraint may be deleted, or values for designated “edit ” variables may be suggested. Currently, QOCA supports linear arithmetic constraints and two different metrics: the square of the Euclidean distance and Manhattan distance. It provides three solvers, all of which rely on keeping the constraints in solved form and relies on novel algorithms for efficient resolving of constraints during direct manipulation. We provide a thorough evaluation of QOCA, both of the interface design and the speed of constraint solving.
SelfOrganizing Graphs  A Neural Network Perspective of Graph Layout
 In Neural Computers, 393–406, ECKMILLER
, 1998
"... The paper presents selforganizing graphs, a novel approach to graph layout based on a competitive learning algorithm. This method is an extension of selforganization strategies known from unsupervised neural networks, namely from Kohonen's selforganizing map. Its main advantage is that it is very ..."
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Cited by 9 (0 self)
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The paper presents selforganizing graphs, a novel approach to graph layout based on a competitive learning algorithm. This method is an extension of selforganization strategies known from unsupervised neural networks, namely from Kohonen's selforganizing map. Its main advantage is that it is very flexibly adaptable to arbitrary types of visualization spaces, for it is explicitly parameterized by a metric model of the layout space. Yet the method consumes comparatively little computational resources and does not need any heavyduty preprocessing. Unlike with other stochastic layout algorithms, not even the costly repeated evaluation of an objective function is required. To our knowledge this is the first connectionist approach to graph layout. The paper presents applications to 2Dlayout as well as to 3Dlayout and to layout in arbitrary metric spaces, such as networks on spherical surfaces. 1 Introduction Automatic layout techniques are a crucial component for any application which...
A Modular Geometric Constraint Solver for User Interface Applications
 In Proc. ACM UIST
, 2001
"... Constraints have been playing an important role in the user interface field since its infancy. A prime use of constraints in this field is to automatically maintain geometric layouts of graphical objects. To facilitate the construction of constraintbased user interface applications, researchers hav ..."
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Cited by 8 (0 self)
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Constraints have been playing an important role in the user interface field since its infancy. A prime use of constraints in this field is to automatically maintain geometric layouts of graphical objects. To facilitate the construction of constraintbased user interface applications, researchers have proposed various constraint satisfaction methods and constraint solvers. Most previous research has focused on either local propagation or linear constraints, excluding more general nonlinear ones. However, nonlinear geometric constraints are practically useful to various user interfaces, e.g., drawing editors and information visualization systems. In this paper, we propose a novel constraint solver called Chorus, which realizes various powerful nonlinear geometric constraints such as Euclidean geometric, nonoverlapping, and graph layout constraints. A key feature of Chorus is its module mechanism that allows users to define new kinds of geometric constraints. Also, Chorus supports "soft" constraints with hierarchical strengths or preferences (i.e., constraint hierarchies). We describe its framework, algorithm, implementation, and experimental results. KEYWORDS: geometric constraints, soft constraints, constraint solvers, module mechanisms, graph layouts
Topology Preserving Constrained Graph Layout
"... Abstract. Constrained graph layout is a recent generalisation of forcedirected graph layout which allows constraints on node placement. We give a constrained graph layout algorithm that takes an initial feasible layout and improves it while preserving the topology of the initial layout. The algorith ..."
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Cited by 7 (3 self)
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Abstract. Constrained graph layout is a recent generalisation of forcedirected graph layout which allows constraints on node placement. We give a constrained graph layout algorithm that takes an initial feasible layout and improves it while preserving the topology of the initial layout. The algorithm supports polyline connectors and clusters. During layout the connectors and cluster boundaries act like impervious rubberbands which try to shrink in length. The intended application for our algorithm is dynamic graph layout, but it can also be used to improve layouts generated by other graph layout techniques. 1