On the 2-Layer Window Width Minimization Problem

Bekos, Michael A.; Förster, Henry; Kaufmann, Michael; Kobourov, Stephen G.; Kryven, Myroslav; Axel, Kuckuk,; Schlipf, Lena

doi:10.1007/978-3-031-23101-8_14

Cited by 2 publications

(2 citation statements)

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“…the smallest x-interval that contains a parent and all its children, over all parents. Bekos et al [4] show that minimizing the maximum window size can be solved efficiently when the children C are fixed and the parents P can be placed, and is NPhard when the parents are fixed and the children can be placed. Note that this asymmetry is due to the windows being defined only for parents P .…”

Section: Introductionmentioning

confidence: 99%

“…Note that this asymmetry is due to the windows being defined only for parents P . As a side effect of the underlying greedy approach, the algorithm of Bekos et al [4] often results in a much larger than optimal average window size in order to minimize the max window. So if the max window exceeds the display size, many parents may have windows that exceed that size.…”

Section: Introductionmentioning

confidence: 99%

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Visualization of Bipartite Graphs in Limited Window Size

Efrat,

Evans,

Köck

et al. 2024

Preprint

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Bipartite graphs are commonly used to visualize objects and their features. An object may possess several features and several objects may share a common feature.The standard visualization of bipartite graphs, with objects and features on two (say horizontal) parallel lines at integer coordinates and edges drawn as line segments, can often be difficult to work with. A common task in visualization of such graphs is to consider one object and all its features. This naturally defines a drawing window, defined as the smallest interval that contains the x-coordinates of the object and all its features. We show that if both objects and features can be reordered, minimizing the average window size is NP-hard. However, if the features are fixed, then we provide an efficient polynomial time algorithm for arranging the objects, so as to minimize the average window size. Finally, we introduce a different way of visualizing the bipartite graph, by placing the nodes of the two parts on two concentric circles. For this setting we also show NP-hardness for the general case and a polynomial time algorithm when the features are fixed.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%