Metro map layout using multicriteria optimization

Stott, J.M.; Rodgers, Peter

doi:10.1109/iv.2004.1320168

Cited by 27 publications

(42 citation statements)

References 5 publications

(6 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…All of them rely on some underlying optimization machinery, which is tuned in order to get drawings that fulfill the above rules as best as possible. The method of Hong et al [15] is based on a spring embedder, the method of Stott and Rodgers [30] uses hill climbing, and the method of Nöllenburg and Wolff [25] relies on mixed-integer programming.…”

Section: Methodsmentioning

confidence: 99%

“…Each of the rules is either implicit or explicit in at least two of the papers of Hong et al [15], Stott and Rodgers [30], and Nöllenburg and Wolff [25], whose algorithms we will discuss in the next section. The reader is invited to study the book of Ovenden [26], which contains an abundance of subway maps from all over the world, in order to make up his own mind as to which set of rules is the right one.…”

Section: Rulesmentioning

confidence: 99%

“…They are computed incrementally by a simulatedannealing-like local-optimization algorithm. The second method, by Stott and Rodgers [30], uses multi-criteria optimization based on hill climbing, a popular generalpurpose local-optimization technique. The third method, by Nöllenburg and Wolff [25], relies on mixed-integer programming, a widely used global-optimization technique.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Drawing Subway Maps: A Survey

Wolff

2007

Informatik Forsch. Entw.

View full text Add to dashboard Cite

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 mediumsize networks can be drawn. Finally we give evidence why drawing good subway maps is difficult (even without labels).

show abstract

Section: Methodsmentioning

confidence: 99%

Section: Rulesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Drawing Subway Maps: A Survey

Wolff

2007

Informatik Forsch. Entw.

View full text Add to dashboard Cite

show abstract

“…Closely related to the first step are the works of Hong et al [8], Merrick and Gudmundsson [11], Nöllenburg and Wolff [12] and Stott and Rodgers [14]. The map labeling problem has also attracted the interest of several researchers.…”

Section: Introductionmentioning

confidence: 99%

Two Polynomial Time Algorithms for the Metro-line Crossing Minimization Problem

et al. 2009

View full text Add to dashboard Cite

Abstract. The metro-line crossing minimization (MLCM) problem was recently introduced in [5] as a response to the problem of drawing metro maps or public transportation networks, in general. According to this problem, we are given a planar, embedded graph G = (V, E) and a set L of simple paths on G, called lines. The main task is to place the lines on the embedding of G, so that the number of crossings among pairs of lines is minimized. Our main contribution is two polynomial time algorithms. The first solves the general case of the MLCM problem, where the lines that traverse a particular vertex of G are allowed to use any side of it to either "enter" or "exit", assuming that the endpoints of the lines are located at vertices of degree one. The second one -which is more efficient in terms of time complexity-solves the restricted case, where only the left and the right side of each vertex can be used. To the best of our knowledge, this is the first time where the general case of the MLCM problem is solved. Previous work in the graph drawing literature was devoted to the restricted case of the MLCM problem under the additional assumption that the endpoints of the lines are either the topmost or the bottommost in their corresponding vertices, i.e., they are either on top or below the lines that pass through the vertex. Even for this case, we improve a known result of Asquith et al. [3] from O(|E| 5/2 |L| 3 ) to O(|V |(|E| + |L|)).

show abstract

“…Lauther and Stübinger [8], and subsequently Brandes et al [2], investigated the problem of generating orthogonal schematic plans from sketch drawings. Hong et al [7], Stott and Rodgers [13] and Nöllenburg and Wolff [12] looked at the layout of metro maps, in which lines generally conform to horizontal, vertical and diagonal (45 • and 135 • ) orientations.…”

Section: Introductionmentioning

confidence: 99%

Schematisation of Tree Drawings

2007

View full text Add to dashboard Cite

Abstract. Given a tree T spanning a set of points S in the plane, we study the problem of drawing T using only line segments aligned with a fixed set of directions C. The vertices in the drawing must lie within a given distance r of each original point p ∈ S, and an objective function counting the number of bends must be minimised. We propose five versions of this problem using different objective functions, and algorithms to solve them. This work has potential applications in geographic map schematisation and metro map layout.

show abstract

Metro map layout using multicriteria optimization

Cited by 27 publications

References 5 publications

Drawing Subway Maps: A Survey

Drawing Subway Maps: A Survey

Two Polynomial Time Algorithms for the Metro-line Crossing Minimization Problem

Schematisation of Tree Drawings

Contact Info

Product

Resources

About