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Algorithm Animation Over the World Wide Web
 In Proc. Int. Workshop on Advanced Visual Interfaces
, 1996
"... In this paper we propose a new model, called Mocha, for providing algorithm animation over the World Wide Web. Mocha is a distributed model with a clientserver architecture that optimally partitions the software components of a typical algorithm animation system, and leverages the power of the Java ..."
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Cited by 23 (2 self)
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In this paper we propose a new model, called Mocha, for providing algorithm animation over the World Wide Web. Mocha is a distributed model with a clientserver architecture that optimally partitions the software components of a typical algorithm animation system, and leverages the power of the Java language, an emerging standard for distributing interactive platformindependent applications across the Web. Mocha provides high levels of security, protects the algorithm code, places a light communication load on the Internet, and allows users with limited computing resources to access animations of computationally expensive algorithms. The user interface combines fast responsiveness and user friendliness with the powerful authoring capabilities of hypertext narratives. We describe the architecture of Mocha and show its advantages over previous methods for algorithm animation over the Internet. We also present a prototype of an animation system for geometric algorithms that can be access...
Graph Drawing
 Lecture Notes in Computer Science
, 1997
"... INTRODUCTION Graph drawing addresses the problem of constructing geometric representations of graphs, and has important applications to key computer technologies such as software engineering, database systems, visual interfaces, and computeraideddesign. Research on graph drawing has been conducte ..."
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Cited by 14 (3 self)
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INTRODUCTION Graph drawing addresses the problem of constructing geometric representations of graphs, and has important applications to key computer technologies such as software engineering, database systems, visual interfaces, and computeraideddesign. Research on graph drawing has been conducted within several diverse areas, including discrete mathematics (topological graph theory, geometric graph theory, order theory), algorithmics (graph algorithms, data structures, computational geometry, vlsi), and humancomputer interaction (visual languages, graphical user interfaces, software visualization). This chapter overviews aspects of graph drawing that are especially relevant to computational geometry. Basic definitions on drawings and their properties are given in Section 1.1. Bounds on geometric and topological properties of drawings (e.g., area and crossings) are presented in Section 1.2. Section 1.3 deals with the time complexity of fundamental graph drawin
Proximity Drawings of Outerplanar Graphs
, 1996
"... A proximity drawing of a graph is one in which pairs of adjacent vertices are drawn relatively close together according to some proximity measure while pairs of nonadjacent vertices are drawn relatively far apart. The fundamental question concerning proximity drawability is: Given a graph G and a d ..."
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Cited by 11 (4 self)
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A proximity drawing of a graph is one in which pairs of adjacent vertices are drawn relatively close together according to some proximity measure while pairs of nonadjacent vertices are drawn relatively far apart. The fundamental question concerning proximity drawability is: Given a graph G and a definition of proximity, is it possible to construct a proximity drawing of G? We consider this question for outerplanar graphs with respect to an infinite family of proximity drawings called fidrawings. These drawings include as special cases the wellknown Gabriel drawings (when fi = 1), and relative neighborhood drawings (when fi = 2). We first show that all biconnected outerplanar graphs are fidrawable for all values of fi such that 1 fi 2. As a side effect, this result settles in the affirmative a conjecture by Lubiw and Sleumer [20, 22], that any biconnected outerplanar graph admits a Gabriel drawing. We then show that there exist biconnected outerplanar graphs that do not admit any...
Optimal Polygonal Representation of Planar Graphs
"... Abstract. In this paper, we consider the problem of representing graphs by polygons whose sides touch. We show that at least six sides per polygon are necessary by constructing a class of planar graphs that cannot be represented by pentagons. We also show that the lower bound of six sides is matched ..."
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Cited by 10 (9 self)
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Abstract. In this paper, we consider the problem of representing graphs by polygons whose sides touch. We show that at least six sides per polygon are necessary by constructing a class of planar graphs that cannot be represented by pentagons. We also show that the lower bound of six sides is matched by an upper bound of six sides with a linear time algorithm for representing any planar graph by touching hexagons. Moreover, our algorithm produces convex polygons with edges with slopes 0, 1,1. 1
Threshold Functions for Random Graphs on a Line Segment
 Combinatorics, Probability and Computing
, 2001
"... We look at a model of random graphs suggested by Gilbert: given an integer n and δ > 0, scatter n vertices independently and uniformly on a metric space, and then add edges connecting pairs of vertices of distance less than δ apart. We consider the asymptotics... ..."
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Cited by 6 (0 self)
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We look at a model of random graphs suggested by Gilbert: given an integer n and δ > 0, scatter n vertices independently and uniformly on a metric space, and then add edges connecting pairs of vertices of distance less than δ apart. We consider the asymptotics...
Area Requirement of Gabriel Drawings
, 1996
"... In this paper we investigate the area requirement of proximity drawings and we prove an exponential lower bound. Namely, our main contribution is to show the existence of a class of Gabrieldrawable graphs that require exponential area for any Gabriel drawing and any resolution rule. Also, we extend ..."
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Cited by 5 (4 self)
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In this paper we investigate the area requirement of proximity drawings and we prove an exponential lower bound. Namely, our main contribution is to show the existence of a class of Gabrieldrawable graphs that require exponential area for any Gabriel drawing and any resolution rule. Also, we extend the result to an infinite class of proximity drawings.
Empty Region Graphs
"... A family of proximity graphs, called Empty Region Graphs (ERG) is presented. The vertices of an ERG are points in the plane, and two points are connected if their neighborhood, defined by a region, does not contain any other point. The region defining the neighborhood of two points is a parameter of ..."
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Cited by 5 (0 self)
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A family of proximity graphs, called Empty Region Graphs (ERG) is presented. The vertices of an ERG are points in the plane, and two points are connected if their neighborhood, defined by a region, does not contain any other point. The region defining the neighborhood of two points is a parameter of the graph. This way of defining graphs is not new, and ERGs include several known proximity graphs such as Nearest Neighbor Graphs, βSkeletons or ΘGraphs. The main contribution is to provide insight and connections between the definition of ERG and the properties of the corresponding graphs. We give conditions on the region defining an ERG to ensure a number of properties that might be desirable in applications, such as planarity, connectivity, trianglefreeness, cyclefreeness, bipartiteness and bounded degree. These conditions take the form of what we call tight regions: maximal or minimal regions that a region must contain or be contained in to make the graph satisfy a given property. We show that every monotone property has at least one corresponding tight region; we discuss possibilities and limitations of this general model for constructing a graph from a point set. 1
Advances in the Theory and Practice of Graph Drawing
 Theor. Comp. Sci
, 1996
"... The visualization of conceptual structures is a key component of support tools for complex applications in science and engineering. Foremost among the visual representations used are drawings of graphs and ordered sets. In this talk, we survey recent advances in the theory and practice of graph d ..."
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Cited by 4 (0 self)
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The visualization of conceptual structures is a key component of support tools for complex applications in science and engineering. Foremost among the visual representations used are drawings of graphs and ordered sets. In this talk, we survey recent advances in the theory and practice of graph drawing. Specific topics include bounds and tradeoffs for drawing properties, threedimensional representations, methods for constraint satisfaction, and experimental studies. 1 Introduction In this paper, we survey selected research trends in graph drawing, and overview some recent results of the author and his collaborators. Graph drawing addresses the problem of constructing geometric representations of graphs, a key component of support tools for complex applications in science and engineering. Graph drawing is a young research field that has growth very rapidly in the last decade. One of its distinctive characteristics is to have furthered collaborative efforts between computer scien...
Drawable and Forbidden Minimum Weight Triangulations (Extended Abstract)
"... A graph is minimum weight drawable if it admits a straightline drawing that is a minimum weight triangulation of the set of points representing the vertices of the graph. In this paper we consider the problem of characterizing those graphs that are minimum weight drawable. Our contribution is twofo ..."
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Cited by 2 (0 self)
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A graph is minimum weight drawable if it admits a straightline drawing that is a minimum weight triangulation of the set of points representing the vertices of the graph. In this paper we consider the problem of characterizing those graphs that are minimum weight drawable. Our contribution is twofold: We show that there exist infinitely many triangulations that are not minimum weight drawable. Furthermore, we present nontrivial classes of triangulations that are minimum weight drawable, along with corresponding linear time (real RAM) algorithms that take as input any graph from one of these classes and produce as output such a drawing. One consequence of our work is the construction of triangulations that are minimum weight drawable but none of which is Delaunay drawablethat is, drawable as a Delaunay triangulation. 1 Introduction and Overview Recently much attention has been devoted to the study of combinatorial properties of wellknown geometric structuresoften referred to a...
Visualizing Geometric Algorithms over the Web
 In Proc. 12th Annu. ACM Sympos. Comput. Geom
, 1997
"... The visual nature of geometry applications makes it a natural area where visualization can be an effective tool for demonstrating algorithms. In this paper we propose a new model, called Mocha, for interactive visualization of algorithms over the World Wide Web. Mocha is a distributed model with ..."
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Cited by 1 (0 self)
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The visual nature of geometry applications makes it a natural area where visualization can be an effective tool for demonstrating algorithms. In this paper we propose a new model, called Mocha, for interactive visualization of algorithms over the World Wide Web. Mocha is a distributed model with a clientserver architecture that optimally partitions the software components of a typical algorithm execution and visualization system, and leverages the power of the Java language, which has become the standard for distributing interactive platformindependent applications across the Web. Mocha provides high levels of security, protects the algorithm code, places a light communication load on the Internet, and allows users with limited computing resources to access executions of computationally expensive algorithms. The user interface combines fast responsiveness with the powerful authoring capabilities of hypertext narratives. We describe the architecture of Mocha, show its advan...