Drawing Subway Maps: A?Survey

This paper deals with automating the drawing of subway maps. There are two features of schematic subway maps that make them different from drawings of other networks such as flow charts or organigrams. First, most schematic subway maps use not only horizontal and vertical lines, but also diagonals. This gives more flexibility in the layout process, but it also makes the problem provably hard. Second, a subway map represents a network whose components have geographic locations that are roughly known to the users of such a map. This knowledge must be respected during the search for a clear layout of the network. For the sake of visual clarity the underlying geography may be distorted, but it must not be given up, otherwise map users will be hopelessly confused. In this paper we first give a rather generally accepted list of rules that should be adhered to by a good subway map. Next we survey three recent methods for drawing subway maps, analyze their performance with respect to the above rules, and compare the resulting maps among each other and to official subway maps drawn by graphic designers. We then focus on one of the methods, which is based on mixed-integer linear programming, a widely-used global optimization technique. This method guarantees to find a drawing that fulfills a subset of the above-mentioned rules (if such a drawing exists) and optimizes a weighted sum of costs that correspond to the remaining rules. The method can draw even large subway networks such as the London Underground in an aesthetically pleasing manner, similar to maps made by professional graphic designers. If station labels are included in the optimization process, so far only medium-size networks can be drawn. Finally we give evidence why drawing good subway maps is difficult (even without labels).     

Interpretations of graphs by university biology students and practicing scientists: Toward a social practice view of scientific representation practices

Using graphs is a key social practice of professional science. As part of a research program that investigates the development of graphing practices from elementary school to professional science activities, this study was designed to investigate similarities and differences in graph‐related interpretations between scientists and college students engaged in collective graph interpretation. Forty‐five students in a second‐year university ecology course and four scientists participated in the study. Guided by domain‐ specific concerns, scientists' graph‐related activities were characterized by a large number of experience‐based, domain‐specific interpretive resources and practices. Students' group based activities were characterized by the lack of linguistic distinctions (between scientific terms) which led to ambiguities in group negotiations; there was also a lack of knowledge about specific organism populations which helped field ecologists construct meaning. Many students learned to provide correct answers to specific graphing questions but did not come to make linguistic distinctions or increase their knowledge of specific populations. In the absence of concerns other than to do well in the course, students did not appear to develop any general interpretive skills for graphs, but learned instead to apply the professor's interpretation. This is problematic because, as we have demonstrated, there are widely differing viable interpretations of the graph. Suggestions for changes in learning environments for graphing that should alleviate this problem are made. © 1999 John Wiley & Sons, Inc. J Res Sci Teach 36: 1020–1043, 1999