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 constraint-based 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, non-overlapping, 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

We address in this paper the problem of constructing embeddings of planar graphs satisfying declarative, user-defined topological constraints. The constraints consist each of a cycle...

The planarization method has proven to be successful in graph drawing. The output, a combinatorial planar embedding of the so-called planarized graph, can be combined with state-of-the-art planar drawing algorithms. However, many practical applications have additional constraints on the drawings that result in restrictions on the set of admissible planar embeddings. In this paper, we consider embedding constraints that restrict the admissible order of incident edges around a vertex. Such constraints occur in applications, e.g., from side or port constraints. We introduce a set of hierarchical embedding constraints that include grouping, oriented, and mirror constraints, and show how these constraints can be integrated into the planarization method. For this, we first present a linear time algorithm for testing if a given graph G is ec-planar, i.e., admits a planar embedding satisfying the given embedding constraints. In the case that G is ec-planar, we provide a linear time algorithm for computing the corresponding ec-embedding. Otherwise, an ec-planar subgraph is computed. The critical part is to re-insert the deleted edges subject to the embedding constraints so that the number of crossings is kept small. For this, we present a linear time algorithm which is able to insert an edge into an ec-planar graph H so that the insertion is crossing minimal among all ec-planar embeddings of H. As a side result, we characterize the set of all possible ec-planar embeddings using BC- and SPQR-trees.

We study the following problem: Given a planar graph G and a planar drawing (embedding) of a subgraph of G, can such a drawing be extended to a planar drawing of the entire graph G? This problem fits the paradigm of extending a partial solution to a complete one, which has been studied before in many different settings. Unlike many cases, in which the presence of a partial solution in the input makes hard an otherwise easy problem, we show that the planarity question remains polynomial-time solvable. Our algorithm is based on several combinatorial lemmata which show that the planarity of partially embedded graphs meets the “oncas” behaviour – obvious necessary conditions for planarity are also sufficient. These conditions are expressed in terms of the interplay between (a) rotation schemes and containment relationships between cycles and (b) the decomposition of a graph into its connected, biconnected, and triconnected components. This implies that no dynamic programming is needed for a decision algorithm and that the elements of the decomposition can be processed independently. Further, by equipping the components of the decomposition with suitable data structures and by carefully splitting the problem into simpler subproblems, we improve our algorithm to reach linear-time complexity. Finally, we consider several generalizations of the problem, e.g. minimizing the number of edges of the partial embedding that need to be rerouted to extend it, and argue that they are NP-hard. Also, we show how our algorithm can be applied to solve related Graph Drawing problems.

More powerful personal computers and higher network bandwidth has meant that graphics has become increasingly important on the web. Graph-based diagrams are one of the most important types of structured graphical information.

For applications which generate diagrammatic representations automatic layout techniques are a crucial component. Since graph-like network diagrams are among the most commonly used and most important types of diagrammatic displays, layout techniques for graphs have been extensively studied. However, a problem with current graph layout methods which are capable of producing satisfactory results for a wide range of graphs is that they often put an extremely high demand on computational resources. This paper introduces a new layout method that consumes only little computational resources and does not need any heavyduty preprocessing. Unlike other declarative layout algorithms not even the costly repeated evaluation of an objective function is required. The method presented is based on a competitive learning algorithm which is an extension of self-organization strategies known from unsupervised neural networks. 1 Introduction For applications which generate diagrammatic representations a...

Constraint logic programming (CLP) is a multidisciplinary research area which can be located between Artificial Intelligence, Operation Research, and Programming Languages, and has to do with modeling, solving, and programming real-life problems which can be described as a set of statements (the constraints) which describe some relationship between the problem's variables. This survey paper gives a brief introduction to C(L)P, presents a (necessarily partial) state of the art in CLP research and applications, points out some promising directions for future applications, and discusses how to cope with current research challenges.

Graph drawing is an information visualization technology for illustrating relations between objects. Interactive graph drawing is often important since it is di#cult to statically lay out complex graphs. For the interactive drawing of general undirected graphs, we previously proposed the high-dimensional approach, which used static graph layouts in high-dimensional spaces to dynamically find two-dimensional layouts according to user interaction. Although the resulting interactive graph drawing method was fast, it imposed a limitation on the successive manipulation of dense parts of graphs. In this paper, we propose an extended method to tackle the limitation. Our new method enables multiple graph nodes to be controlled simultaneously in interactive graph drawing. For this purpose, we extend the underlying constraint programming mechanism by introducing the notion of soft constraints as well as by using additional constraints on multiple controlled nodes.

Abstract. Current practice in adaptation modeling assumes that concepts and relationships between concepts are the fundamental building blocks of any adaptive course or adaptive application. This assumption underlies many of the mismatches we nd between the syntax of an adaptation model and the semantics of the `realworld' entity it is trying to model, e.g. procedural knowledge modeled as a single concept and services or activities modeled as pockets of intelligent content. Furthermore, it results in adaptation models that are devoid of truly interactive services with work ow and data ow between those services; it is impossible to capture the semantics of a process-oriented application, e.g. activity-based learning in education and Standard Operating Procedures (SOPs) in the workplace. To this end, we describe a representation of a conceptual and service-based adaptation model. The most signi cant departure from existing representations for adaptation models is the rei cation of services. The goal is to allow for the adaptation of the process itself and not just its constituent parts, e.g. an SOP can be adapted to the role or job function of a user. This expressive power will address the mismatches identi ed above and allow for activity-based and process-oriented adaptive applications. 1