An Interactive Multi-user System for Simultaneous Graph Drawing

Kobourov, Stephen G.; Pitta, Chandan

doi:10.1007/978-3-540-31843-9_51

Cited by 9 publications

(9 citation statements)

References 16 publications

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“…Recently, a new direction in the area of the graph drawing has been opened: Simultaneous planar graph drawing [1,[3][4][5][6]. Consider a set of objects with two different sets of relations.…”

Section: Introductionmentioning

confidence: 99%

Two trees which are self-intersecting when drawn simultaneously

Geyer

Kaufmann

Vrťo

2009

Discrete Mathematics

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A current topic in graph drawing is the question how to draw two edge sets on the same vertex set, the so-called simultaneous drawing of graphs. The goal is to simultaneously find a nice drawing for both of the sets. It has been found out that only restricted classes of planar graphs can be drawn simultaneously using straight lines and without crossings within the same edge set. In this paper, we negatively answer one of the most often posted open questions namely whether any two trees with the same vertex set can be drawn simultaneously crossing-free in a straight-line way.

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Section: Introductionmentioning

confidence: 99%

Two trees which are self-intersecting when drawn simultaneously

Geyer

Kaufmann

Vrťo

2009

Discrete Mathematics

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“…Kobourov and Pitta [20] presented an interactive multiuser system for drawing graphs simultaneously. Their system uses the help of the human viewer and a rudimentary crossing minimization heuristic to minimize the number of crossings in a straight-line drawing of two graphs simultaneously.…”

Section: Preliminariesmentioning

confidence: 99%

Crossing Minimization meets Simultaneous Drawing

Chimani

Jünger

Schulz

2008

2008 IEEE Pacific Visualization Symposium

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We define the concept of crossing numbers for simultaneous graphs by extending the crossing number problem of traditional graphs. We discuss differences to the traditional crossing number problem, and give an NP-completeness proof and lower and upper bounds for the new problem. Furthermore, we show how existing heuristic and exact algorithms for the traditional problem can be adapted to the new task of simultaneous crossing minimization, and report on a brief experimental study of their implementations.

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“…For non-planar graphs, force-directed techniques are used by Erten et al to define visualization schemes and design drawing heuristics where vertices shared by many graphs of the sequence are located in the center of the layout and edges shared by many graphs are not too long [16]. Kobourov and Pitta describe an interactive multi-user environment for simultaneous embedding where the number of edge crossings is kept under control by means of heuristic primitives [23]. Chimani et al further investigate the problem of minimizing the number of crossings in a simultaneous embedding; they show the NP-hardness of the question and experimentally compare heuristics and exact drawing algorithms [7].…”

Section: Graph Drawing Algorithmsmentioning

confidence: 99%

“…However, since G pag and G usr share the whole vertex set, the centrality of the shared vertices (considered in [16]) is not a meaningful aesthetic requirement in our case. Also, motivated by recent cognitive experiments, we do not insist on minimizing the number of edge crossings (as done in [7,23]) but rather we try to control the visual quality of the edge crossings. More precisely, human-computer interaction experiments have shown that orthogonal crossings do not inhibit human task performance when reading a drawing and that users have a geodesic tendency when discovering relations between pairs of vertices [20,21,22].…”

Section: Graph Drawing Algorithmsmentioning

confidence: 99%

A Graph Drawing Application to Web Site Traffic Analysis

Didimo¹,

Liotta²,

Romeo³

2011

JGAA

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Web site traffic analysis studies how different pages forming Web sites are accessed by their target audience over time. From a business intelligence point of view, it represents one of the key activities for many private companies and public institutions. Recent papers pointed out that Web site traffic analysis is especially useful if it focuses on the user interest into the relevant concepts described in a Web site rather than counting user accesses to the distinct pages forming the Web site. This paper extends existing measures of conceptual Web site traffic analysis and describes a new system that supports this analysis by means of graph visualization techniques. The graph drawing engine of the system is a force-directed heuristic that computes a simultaneous embedding of two suitably defined graphs, that are non-planar in general. The heuristic is especially designed to take into account two important aesthetic criteria of the drawing: crossing resolution and geodesic edge tendency. We also present some experiments and case studies to show the effectiveness of the proposed approach in practice.

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An Interactive Multi-user System for Simultaneous Graph Drawing

Cited by 9 publications

References 16 publications

Two trees which are self-intersecting when drawn simultaneously

Two trees which are self-intersecting when drawn simultaneously

Crossing Minimization meets Simultaneous Drawing

A Graph Drawing Application to Web Site Traffic Analysis

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