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A Fast MultiScale Method for Drawing Large Graphs
 JOURNAL OF GRAPH ALGORITHMS AND APPLICATIONS
, 2002
"... We present a multiscale layout algorithm for the aesthetic drawing of undirected graphs with straightline edges. The algorithm is extremely fast, and is capable of drawing graphs that are substantially larger than those we have encountered in prior work. For example, the paper contains a drawi ..."
Abstract

Cited by 79 (10 self)
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We present a multiscale layout algorithm for the aesthetic drawing of undirected graphs with straightline edges. The algorithm is extremely fast, and is capable of drawing graphs that are substantially larger than those we have encountered in prior work. For example, the paper contains a drawing of a graph with over 15,000 vertices. Also we achieve "nice" drawings of 1000 vertex graphs in about 1 second. The proposed algorithm embodies a new multiscale scheme for drawing graphs, which was motivated by the earlier multiscale algorithm of Hadany and Harel [HH99]. In principle, it could significantly improve the speed of essentially any forcedirected method (regardless of that method's ability of drawing weighted graphs or the continuity of its costfunction).
ACE: A Fast Multiscale Eigenvector Computation for Drawing Huge Graphs
, 2002
"... We present an extremely fast graph drawing algorithm for very large graphs, which we term ACE (for Algebraic multigrid Computation of Eigenvectors). ACE finds an optimal drawing by minimizing a quadratic energy function due to Hall, using a novel algebraic multigrid technique. The algorithm exhibits ..."
Abstract

Cited by 62 (13 self)
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We present an extremely fast graph drawing algorithm for very large graphs, which we term ACE (for Algebraic multigrid Computation of Eigenvectors). ACE finds an optimal drawing by minimizing a quadratic energy function due to Hall, using a novel algebraic multigrid technique. The algorithm exhibits an improvement of something like two orders of magnitude over the fastest algorithms we are aware of; it draws graphs of a million nodes in less than a minute. Moreover, the algorithm can deal with more general entities, such as graphs with masses and negative weights (to be defined in the text), and it appears to be applicable outside of graph drawing too.
A Fast Multi Method for Drawing Large Graphs
 Journal of Graph Algorithms and Applications
, 2001
"... We present a mu ltiscale layou algorithm for the aesthetic drawing ofuV#860L32 graphs with straightline edges. The algorithm is extremely fast, and is capable of drawing graphs that aresuSVV tially larger than those we haveencou tered in prior work. For example, the paper contains a drawing of ..."
Abstract
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We present a mu ltiscale layou algorithm for the aesthetic drawing ofuV#860L32 graphs with straightline edges. The algorithm is extremely fast, and is capable of drawing graphs that aresuSVV tially larger than those we haveencou tered in prior work. For example, the paper contains a drawing of a graph with over 15,000 vertices. Also we achieve "optimal" drawings of 1000 vertex graphs in ab ou 1 second. The proposed algorithm embodies a new mu ltiscale scheme for drawing graphs, which was motivated by the earlier muS8820L4# algorithm of Hadany and Harel [HH99]. In principle, it cou# significantly improve the speed of essentially any forcedirected method (regardless of that method's ability of drawing weighted graphs or the continu0 y of its costfuL436280 1 Introducti7 AgraphG(V,E) is an abstract structure that is used to model a relation over a set V ofen tities. Graph drawin is acon ven tion# tool for the visualization of relationq in]4#]Rq]#] an its usefulnRq depenV on its readability, that is, the capability of con veyin the meanfi# of the diagram quickly # A shorter version appeared in Proc. GraphD awing 2000, LNCS 1984, pp. 183196, Springer Verlag, 2000. clearly. In recen t years, man y algorithms for drawin graphs automatically were proposed (the state of the art is surveyedcomprehen]8 ely in 99, KW01]). Wecon#E trateon the problem of drawin an unF8ERqfi4 graph with straightlin edges. In this case the problem reduces to that of positionRq the vertices bydeterminfiF a mappin L : V R . A populargenrR# approach to this problem is the forcedirected technRVEF which in troduces a heuristic costfunR]F9 (an energy) of themappin L, which (hopefully) achieves its min4 umwhen the layout isn ice. Varian ts of this approach di#er in the defin9fiFR of t...