This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract-We present the results of evaluating four techniques for displaying group or cluster information overlaid on node-link diagrams: node coloring, GMap, BubbleSets, and LineSets. The contributions of the paper are three fold. First, we present quantitative results and statistical analyses of data from an online study in which approximately 800 subjects performed ten types of group and network tasks in the four evaluated visualizations. Specifically, we show that BubbleSets is the best alternative for tasks involving group membership assessment; that visually encoding group information over basic node-link diagrams incurs an accuracy penalty of about 25% in solving network tasks; and that GMap's use of prominent group labels improves memorability. We also show that GMap's visual metaphor can be slightly altered to outperform BubbleSets in group membership assessment. Second, we discuss visual characteristics that can explain the observed quantitative differences in the four visualizations and suggest design recommendations. This discussion is supported by a small scale eye-tracking study and previous results from the visualization literature. Third, we present an easily extensible user study methodology. Permanent repository link
Trees are usually drawn planar, i.e. without any crossings. In this paper, we investigate the area requirement of (non-upward) planar straight-line grid drawings of binary trees. Let T be a binary tree with n nodes. We show that T admits a planar straight-line grid drawing with area O(n) and with any pre-specified aspect ratio in the range [1, n α ], where α is a constant such that 0 ≤ α < 1. We also show that such a drawing can be constructed in O(n log n) time.
Ordered trees are generally drawn using order-preserving planar straight-line grid drawings. We investigate the area-requirements of such drawings and present several results. Let T be an ordered tree with n nodes. We show that:• T admits an order-preserving planar straight-line grid drawing with 0(n log n) area.• If T is a binary tree, then T admits an order-preserving planar straight-line grid drawing with 0(n log log n) area.• If T is a binary tree, then T admits an order-preserving upward planar straight-line grid drawing with optimal 0(n logn) area.We also study the problem of drawing binary trees with user-specified aspect ratios. We show that an ordered binary tree T with n nodes admits an order-preserving planar straight-line grid drawing with area 0(n logn), and any user-specified aspect ratio in the range [l,n/logn]. All the drawings mentioned above can be constructed in 0(n) time. Int. J. Comput. Geom. Appl. 2003.13:487-505. Downloaded from www.worldscientific.com by UNIVERSITY OF NEW HAMPSHIRE on 02/08/15. For personal use only. We assume a 2-dimensional Cartesian space. We assume that this space is covered by an infinite rectangular grid, consisting of horizontal and vertical channels. An order-preserving drawing of T is one in which the counterclockwise ordering of the edges incident on a node is the same as their prespecified ordering in T. A planar drawing of T is one with no edge-crossings. An upward drawing of T is one where each node is placed either at the same y-coordinate as, or at a higher y-coordinate than, the y-coordinates of its children. A straight-line drawing of T is one, where each edge is drawn as a single line segment. A grid drawing of T is one, where each node is assigned integer x-and y-coordinates.Ordered trees are generally drawn using order-preserving planar straight-line grid drawings. An upward drawing is desirable because it makes it easier for the user to determine the parent-child relationships between the nodes.The enclosing rectangle E of a drawing D of T is the smallest rectangle with sides parallel to the x-and j/-axes, respectively, covering the entire drawing. The height h, width w, and area of D is equal to the height, width, and area, respectively, of E. The aspect ratio of D is equal to max{/i,u;}/min{/i, •?/;}.We investigate the area-requirement of the order-preserving planar straight-line grid drawings of ordered trees, and present several results: Let T be an ordered tree with n nodes.Result 1: We show that T admits an order-preserving planar straight-line grid drawing with O(nlogn) area, 0{n) height, and O(logn) width, which can be constructed in 0(n) time. Result 2: If T is a binary tree, then we show stronger results:Result 2a: T admits an order-preserving planar straight-line grid drawing with 0(n log log n) area, 0((n/ log n) log log n) height, and O(logn) width, which can be constructed in 0(n) time. Result 2b: T admits an order-preserving upward planar straight-line grid drawing with optimal O(nlogn) area, 0(n) height, and O(logn) width, which can be ...
CAPTCHAs (completely automated public Turing test to tell computers and humans apart) are in common use today as a method for performing automated human verification online. The most popular type of CAPTCHA is the text recognition variety. However, many of the existing printed text CAPTCHAs have been broken by web-bots and are hence vulnerable to attack. We present an approach to use human-like handwriting for designing CAPTCHAs. A synthetic handwriting generation method is presented, where the generated textlines need to be as close as possible to human handwriting without being writer-specific. Such handwritten CAPTCHAs exploit the differential in handwriting reading proficiency between humans and machines. Test results show that when the generated textlines are further obfuscated with a set of deformations, machine recognition rates decrease considerably, compared to prior work, while human recognition rates remain the same.
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