Showing papers on "Angular resolution (graph drawing) published in 1998"
1 Aug 1998
TL;DR: In this paper, a planar polyline grid drawing of any plane graph with n vertices and maximum degree n on a (2n - 5) × (3 2n - 7/2) grid with at most 5n - 15 bends and minimum angle > 2/d was constructed.
Abstract: We present a linear time algorithm that constructs a planar polyline grid drawing of any plane graph with n vertices and maximum degree n on a (2n - 5) × (3/2n - 7/2) grid with at most 5n - 15 bends and minimum angle > 2/d In the constructed drawings, every edge has at most three bends and length O(n) To our best knowledge, this algorithm achieves the best simultaneous bounds concerning the grid size, angular resolution, and number of bends for planar grid drawings of high-degree planar graphs Besides the nice theoretical features, the practical drawings are aesthetically very pleasing An implementation of our algorithm is available with the AGD-Library (Algorithms for Graph Drawing) [2, 1] Our algorithm is based on ideas by Kant for polyline grid drawings for triconnected plane graphs [23] In particular, our algorithm significantly improves upon his bounds on the angular resolution and the grid size for non-triconnected plane graphs In this case, Kant could show an angular resolution of 4/3d+7 and a grid size of (2n - 5) × (3n - 6), only
75 citations
1 Jan 1998
TL;DR: This algorithm significantly improves upon Kant's bounds on the angular resolution and the grid size for non-triconnected plane graphs and the practical drawings are aesthetically very pleasing.
Abstract: We present a linear time algorithm that constructs a planar polyline grid drawing of any plane graph with n vertices and maximum degree n on a (2n - 5) × (3/2n - 7/2) grid with at most 5n - 15 bends and minimum angle > 2/d. In the constructed drawings, every edge has at most three bends and length O(n). To our best knowledge, this algorithm achieves the best simultaneous bounds concerning the grid size, angular resolution, and number of bends for planar grid drawings of high-degree planar graphs. Besides the nice theoretical features, the practical drawings are aesthetically very pleasing. An implementation of our algorithm is available with the AGD-Library (Algorithms for Graph Drawing) [2, 1]. Our algorithm is based on ideas by Kant for polyline grid drawings for triconnected plane graphs [23]. In particular, our algorithm significantly improves upon his bounds on the angular resolution and the grid size for non-triconnected plane graphs. In this case, Kant could show an angular resolution of 4/3d+7 and a grid size of (2n - 5) × (3n - 6), only.