TY - JOUR

T1 - Planarity-preserving clustering and embedding for large planar graphs

AU - Duncan, Christian A.

AU - Goodrich, Michael T.

AU - Kobourov, Stephen G.

N1 - Funding Information:
✩ A preliminary version of this paper appeared in the Proceedings of the 7th Annual Symposium on Graph Drawing (GD ’99), 1999, pp. 186–196. This research was partially supported by NSF under grant CCR-9732300 and ARO under grant DAAH04-96-1-0013. * Corresponding author. E-mail addresses: duncan@cs.miami.edu (C.A. Duncan), goodrich@ics.uci.edu (M.T. Goodrich), kobourov@cs.arizona.edu (S.G. Kobourov).

PY - 2003/2

Y1 - 2003/2

N2 - In this paper we present a novel approach for cluster-based drawing of large planar graphs that maintains planarity. Our technique works for arbitrary planar graphs and produces a clustering which satisfies the conditions for compound-planarity (c-planarity). Using the clustering, we obtain a representation of the graph as a collection of O(logn) layers, where each succeeding layer represents the graph in an increasing level of detail. At the same time, the difference between two graphs on neighboring layers of the hierarchy is small, thus preserving the viewer's mental map. The overall running time of the algorithm is O(nlogn), where n is the number of vertices of graph G.

AB - In this paper we present a novel approach for cluster-based drawing of large planar graphs that maintains planarity. Our technique works for arbitrary planar graphs and produces a clustering which satisfies the conditions for compound-planarity (c-planarity). Using the clustering, we obtain a representation of the graph as a collection of O(logn) layers, where each succeeding layer represents the graph in an increasing level of detail. At the same time, the difference between two graphs on neighboring layers of the hierarchy is small, thus preserving the viewer's mental map. The overall running time of the algorithm is O(nlogn), where n is the number of vertices of graph G.

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U2 - 10.1016/S0925-7721(02)00094-9

DO - 10.1016/S0925-7721(02)00094-9

M3 - Article

AN - SCOPUS:84867962052

VL - 24

SP - 95

EP - 114

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

IS - 2

ER -