16845895
Refinement of Three-Dimensional Orthogonal Graph Drawings
In this paper we introduce a number of techniques for the refinement of three-dimensional orthogonal drawings of maximum degree six graphs. We have implemented several existing algorithms for three-dimensional orthogonal graph drawing including a number of heuristics to improve their performance. The performance of the refinements on the produced drawings is then evaluated in an extensive experimental study. We measure the aesthetic criteria of the bounding box volume, the average and maximum number of bends per edge, and the average and maximum edge length. On the same set of graphs used in Di Battista et al. [3], our main refinement algorithm improves the above aesthetic criteria by 80%, 38%, 10%, 54% and 49%, respectively.
32158792
An Algorithm for Three-Dimensional Orthogonal Graph Drawing
In this paper we present an algorithm for 3-dimensional orthogonal graph drawing based on the movement of vertices from an initial layout along the main diagonal of a cube. For an n-vertex m-edge graph with maximum degree six, the algorithm produces drawings with bounding box volume at most 2:37n3 and with a total of 7m/3 bends, using no more than 4 bends per edge route. For maximum degree five graphs the bounding box has volume n3 and each edge route has two bends. These results establish new bounds for 3-dimensional orthogonal graph drawing algorithms and improve on some existing bounds.
341729
Lower Bounds for the Number of Bends in Three-Dimensional Orthogonal Graph Drawings
In this paper we present the first non-trivial lower bounds for the total number of bends in 3-D orthogonal drawings of maximum degree six graphs. In particular, we prove lower bounds for the number of bends in 3-D orthogonal drawings of complete simple graphs and multigraphs, which are tight in most cases. These result are used as the basis for the construction of infinite classes of c-connected simple graphs and multigraphs (2 ≤ c ≤ 6) of maximum degree Δ (3 ≤ Δ ≤ 6) with lower bounds on the total number of bends for all members of the class. We also present lower bounds for the number of bends in general position 3-D orthogonal graph drawings. These results have significant ramifications for the '2-bends' problem, which is one of the most important open problems in the field.
123081730
Simultaneous diagonal flips in plane triangulations
Simultaneous diagonal flips in plane triangulations are investigated. It is proved that every triangulation with at least six vertices has a simultaneous flip into a 4-connected triangulation, and that it can be computed in linear time. It follows that every triangulation has a simultaneous flip into a Hamiltonian triangulation. This result is used to prove that for any two n-vertex triangulations, there exists a sequence of O(log n) simultaneous flips to transform one into the other. The total number of edges flipped in this sequence is O(n). The maximum size of a simultaneous flip is then studied. It is proved that every triangulation has a simultaneous flip of at least 1/3(n − 2) edges. On the other hand, every simultaneous flip has at most n − 2 edges, and there exist triangulations with a maximum simultaneous flip of 6/7 (n − 2) edges.
122961893
Lower Bounds for the Number of Bends in Three-Dimensional Orthogonal Graph Drawings
45354174
On the Parameterized Complexity of Layered Graph Drawing
We consider graph drawings in which vertices are assigned to layers and edges are drawn as straight line-segments between vertices on adjacent layers. We prove that graphs admitting crossing-free h-layer drawings (for fixed h) have bounded pathwidth. We then use a path decomposition as the basis for a linear-time algorithm to decide if a graph has a crossing-free h-layer drawing (for fixed h). This algorithm is extended to solve a large number of related problems, including allowing at most k crossings, or removing at most r edges to leave a crossing-free drawing (for fixed k or r). If the number of crossings or deleted edges is a non-fixed parameter then these problems are NP-complete. For each setting, we can also permit downward drawings of directed graphs and drawings in which edges may span multiple layers, in which case the total span or the maximum span of edges can be minimized. In contrast to the so-called Sugiyama method for layered graph drawing, our algorithms do not assume a preassignment of the vertices to layers.
45540830
Image tracking in real-time: a transputer emulation of some early mammalian vision processes
By emulating some of the 'early' vision processes believed to occur in the visual cortex of mammals, dramatic savings can be made in the com­ putational efforts usually associated with image processing. This paper describes the design and implementation of a low-cost visual tracking sys­ tem that uses no special signal processing, vector processing nor floating­ point hardware. Its effectiveness relies only on the parallel replication of fast scaler integer processors with low latency communications. The current implementation uses 10 T425 transputers, processes 544 x 544 byte-pixel images at camera frame rates and provides 100 Hz. tracking feedback signals to the camera pan-and-tilt motors with a latency of no more than one-fifth of a second. The system will track any object that occupies the (majority of the) centre of the field of view moving against any background - no special lighting conditio~s or artificial scenery are required. The design and implementation follow naturally parallel struc­ tures and are expressed at all levels in occam.
5598249
MSW Spaces
12975927
Uniform Interpretations of L Forms
This paper investigates interpretations of L forms in which the substitution defining the interpretation is uniform in terminal letters. Such uniform interpretations have several advantages over the ordinary ones, both from a mathematical and biological point of view. A number of different aspects of uniform interpretations are studied. It is felt that the results will shed new light on the theory of L forms and, in general, on the theory of L systems.
6720403
The visual specification of context
We introduce a simple and novel visual technique for the specification of context in structured documents called T-graphs that we base on T-configurations in document trees. The technique is implemented in the current version of DESIGNER. Although we are applying this technique in the specification of context-dependent style sheets for HTML, XML, and SGML documents, it is clear that it can be used in other environments such as query specification for structured documents and for computer program transformations. We compare T-graphs with the context specification techniques found in other style-sheet systems and we also provide examples of context that we can and cannot specify with T-graphs. Although T-graphs are restrictive, they lend themselves to visual construction and modification, our main requirement when we designed this context specification method. We also investigate the time and space complexity of T-graph matching, a necessity for efficient implementation.
13899040
The Regularity of Two-Way Nondeterministic Tree Automata Languages
We establish that regularly extended two-way nondeterministic tree automata with unranked alphabets have the same expressive power as regularly extended nondeterministic tree automata with unranked alphabets alphabets. We obtain this results by establishing regularly extended versions of a congruence on trees and of a congruence on, so called, views. Our motivation for the study of these tree models is the Extensible Markup Language (XML), a metalanguage for defining document grammars. Such grammars have regular sets of right-hand sides for their productions and tree automata provide an alternative and useful modeling tool for them. In particular, we believe that they provide a useful computational model for what we call caterpillar expressions.