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Capturing Lombardi Flow in Orthogonal Drawings by Minimizing the Number of Segments.
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TLDR
This work investigates the problem of constructing orthogonal drawings where a small number of horizontal and vertical line segments covers all vertices and gives polynomial-time algorithms for upward orthogonic drawings with the minimum number of segments covering the vertices.Abstract:
Inspired by the artwork of Mark Lombardi, we study the problem of constructing orthogonal drawings where a small number of horizontal and vertical line segments covers all vertices. We study two problems on orthogonal drawings of planar graphs, one that minimizes the total number of line segments and another that minimizes the number of line segments that cover all the vertices. We show that the first problem can be solved by a non-trivial modification of the flow-network orthogonal bend-minimization algorithm of Tamassia, resulting in a polynomial-time algorithm. We show that the second problem is NP-hard even for planar graphs with maximum degree 3. Given this result, we then address this second optimization problem for trees and series-parallel graphs with maximum degree 3. For both graph classes, we give polynomial-time algorithms for upward orthogonal drawings with the minimum number of segments covering the vertices.read more
Citations
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Book ChapterDOI
Minimum-Width Drawings of Phylogenetic Trees
TL;DR: It is shown that finding a minimum-width orthogonal upward drawing of a phylogenetic tree is NP-hard for binary trees with unconstrained combinatorial order and an algorithm is provided to provide a linear-time algorithm for ordered trees.
Journal ArticleDOI
Smooth Orthogonal Drawings of Planar Graphs
References
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An $n^{5/2} $ Algorithm for Maximum Matchings in Bipartite Graphs
John E. Hopcroft,Richard M. Karp +1 more
TL;DR: This paper shows how to construct a maximum matching in a bipartite graph with n vertices and m edges in a number of computation steps proportional to $(m + n)\sqrt n $.
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Graph Drawing: Algorithms for the Visualization of Graphs
TL;DR: In this paper, the authors describe fundamental algorithmic techniques for constructing drawings of graphs and provide an accurate, accessible reflection of the rapidly expanding field of graph drawing, using a reference manual.
Proceedings ArticleDOI
A n5/2 algorithm for maximum matchings in bipartite
John E. Hopcroft,Richard M. Karp +1 more
TL;DR: In this paper, a bipartite graph with n vertices and m edges was constructed in a number of computation steps proportional to (m+n) n, where n is the number of edges in the graph.
Book ChapterDOI
Graphviz: Open source graph drawing tools
TL;DR: Graphviz is a heterogeneous collection of graph drawing tools containing batch layout programs, a platform for incremental layout, customizable graph editors, utility programs useful in graph visualization; and libraries for attributed graphs.