How Many Slopes Does Polynomial Area Cost?
This work provides the first systematic study of trade-offs between slopes, bends, and area for planar graph drawings, which is significant for researchers and practitioners in graph drawing and visualization.
This paper investigates the relationship between the number of slopes, bends per edge, and area for planar drawings of bounded-degree graphs. It presents new constructions that achieve polynomial-area drawings with few bends per edge by slightly increasing the number of slopes, addressing a gap where existing methods for higher-degree graphs often required super-polynomial area.
In this work, we study the interplay between the number of slopes, the number of bends per edge, and the area requirements for planar drawings of bounded-degree graphs. Our motivation stems from the fact that, while numerous algorithms produce planar drawings with few slopes for graphs of relatively small degree in polynomial area, existing approaches for higher-degree graphs often require super-polynomial area. We address this gap in the literature by presenting new constructions that yield polynomial-area drawings with few bends per edge while slightly increasing the required number of slopes, thereby providing the first systematic study of slopes, bends and area trade-offs.